SIR  ISAAC  NEWTON 


From  NEWTON 
to  EINSTEIN 

Changing  Conceptions  of 
THE  UNIVERSE 

BY 

BENJAMIN  HARROW,  PH.D. 

SECOND  EDITION,  REVISED  AND  ENLARGED 

WITH  ARTICLES  BY  PROF.  EINSTEIN,  PROF.  J.  S.  AMES 
(JOHNS  HOPKINS),  SIR  FRANK  DYSON  (ASTRONOMER 
ROYAL),  PROF.  A.  S.  EDDINQTON  (CAMBRIDGE)  AND  SIR 
J.  J.  THOMSON  (PRESIDENT  OF  THE  ROYAL  SOCIETY) 

Portraits  and  Illustrations 


NEW  YORK 

D.  VAN  NOSTRAND  COMPANY 

EIGHT  WARREN  STREET 

1920 


First  Edition,  May,  1920 
Second  Edition,  October,  19ZO 

f$& 


Copyright,  1920 

BY 

D.  VAN  NOSTRAND  COMPANY 


PREFACE 


EINSTEIN'S  contributions  to  our  ideas  of  time 
and  space,  and  to  our  knowledge  of  the  universe 
in  general,  are  of  so  momentous  a  nature,  that 
they  easily  take  their  place  among  the  two  or 
three  greatest  achievements  of  the  twentieth  cen- 
tury. This  little  book  attempts  to  give,  in 
popular  form,  an  account  of  this  work.  As, 
however,  Einstein's  work  is  so  largely  dependent 
upon  the  work  of  Newton  and  Newton's  success- 
ors, the  first  two  chapters  are  devoted  to  the 
latter. 

B.H. 


PREFACE  TO  SECOND  EDITION 


THE  preparation  of  this  new  edition  has  made 
it  possible  to  correct  errors,  to  further  amplify 
certain  portions  of  the  text  and  to  enlarge  the 
ever-increasing  bibliography  on  the  subject. 
Photographs  of  Professors  J.  J.  Thomson,  Michel- 
son,  Minkowski  and  Lorentz  are  also  new  features 
in  this  edition. 

The  explanatory  notes  and  articles  in  the 
Appendix  will,  I  believe,  present  no  difficulties  to 
readers  who  have  mastered  the  contents  of  the 
book.  They  are  in  fact  "popular  expositions"  of 
various  phases  of  the  Einstein  theory;  but 
experience  has  shown  that  even  "popular  exposi- 
tions" of  the  theory  need  further  "popular  intro- 
ductions." 

I  wish  to  take  this  opportunity  of  thanking 
Prof.  Einstein,  Prof.  A.  A.  Michelson  of  the 
University  of  Chicago,  Prof.  J.  S.  Ames  of  Johns 
Hopkins  University,  and  Professor  G.  B.  Pegram 
of  Columbia  University  for  help  in  various  ways 
which  they  were  good  enough  to  extend  to  me. 
Prof.  J.  S.  Ames  and  the  editor  of  Science  have 
been  kind  enough  to  allow  me  to  reprint  the  for- 
mer's excellent  presidential  address  on  Einstein's 
theory,  delivered  before  the  members  of  the 
American  Physical  Society. 

B.  H. 


TABLE  OF  CONTENTS 

PAGE 

I.  NEWTON 1 

II.  THE  ETHER  AND  ITS  CONSEQUENCES  .  27 

III.  EINSTEIN 41 

IV.  APPENDIX 81 

Time,  Space  and  Gravitation,  by  Prof. 

Einstein 88 

Einstein's  Law  of  Gravitation,  by  Prof. 

J.  S.  Ames  93 


The  Reflection  of  light  by  Gravitation 
and  the  Einstein  Theory  of  Relativity, 
by  Sir  Frank  Dyson,  Prof.  A.  S.  Ed- 
dington  and  Sir  J.  J.  Thomson  .  . 


NEWTON 

"Newton  was  the  greatest  genius  that  ever 
existed." — Lagrange,  one  of  the  greatest  of  French 
mathematicians. 

"The  efforts  of  the  great  philosopher  were 
always  superhuman;  the  questions  which  he  did 
not  solve  were  incapable  of  solution  in  his  time." 
— Arago,  famous  French  astronomer. 

EINSTEIN 

"This  is  the  most  important  result  obtained  in 
connection  with  the  theory  of  gravitation  since 
Newton's  day.  Einstein's  reasoning  is  the  result 
of  one  of  the  highest  achievements  of  human 
thought." — Sir  J.  J.  Thomson,  president  of  the 
British  Royal  Society  and  professor  of  physics  at 
the  University  of  Cambridge. 

"It  surpasses  in  boldness  everything  previously 
suggested  in  speculative  natural  philosophy  and 
even  in  the  philosophical  theories  of  knowledge. 
The  revolution  introduced  into  the  physical 
conceptions  of  the  world  is  only  to  be  compared 
in  extent  and  depth  with  that  brought  about  by 
the  introduction  of  the  Copernican  system  of 
the  universe." — Prof.  Max  Plancky  professor  of 
physics  at  the  University  of  Berlin  and  winner  of 
the  Nobel  Prize. 


NEWTON 

speaking  of  Newton  we  are  tempted 
to  paraphrase  a  line  from  the  Scrip- 
tures: Before  Newton  the  Solar 
System  was  without  form,  and  void; 
then  Newton  came  and  there  was  light.  To 
have  discovered  a  law  not  only  applicable  to 
matter  on  this  earth,  but  to  the  planets  and  sun 
and  stars  beyond,  is  a  triumph  which  places 
Newton  among  the  super-men. 

What  Newton's  law  of  gravitation  must  have 
meant  to  the  people  of  his  day  can  be  pictured  only 
if  we  conceive  what  the  effect  upon  us  would  be 
if  someone — say  Marconi — were  actually  to 
succeed  in  getting  into  touch  with  beings  on  an- 
other planet.  Newton's  law  increased  confidence 
in  the  universality  of  earthly  laws;  and  it 
strengthened  belief  in  the  cosmos  as  a  law- 
abiding  mechanism. 

Newton's  Law.    The  attraction  between  any 
two  bodies  is  proportional  to  their  masses  and 
inversely  proportional  to  the  square  of  the  dis- 
tance that  separates  them.     This  is  the  concen- 
1 


'  Ffom  Newton  to  Einstein 


trated  form  of  Newton's  law.  If  we  apply  this 
law  to  two  such  bodies  as  the  sun  and  the  earth, 
we  can  state  that  the  sun  attracts  the  earth, 
and  the  earth,  the  sun.  Furthermore,  this 
attractive  power  will  depend  upon  the  distance 
between  these  two  bodies.  Newton  showed 
that  if  the  distance  between  the  sun  and  the 
earth  were  doubled  the  attractive  power  would 
be  reduced  not  to  one-half,  but  to  one-fourth; 
if  trebled,  the  attractive  power  would  be  re- 
duced to  one-ninth.  If,  on  the  other  hand,  the 
distance  were  halved,  the  attractive  power 
would  be  not  merely  twice,  but  four  times  as 
great.  And  what  is  true  of  the  sun  and  the 
earth  is  true  of  every  body  in  the  firmament, 
and,  as  Professor  Rutherford  has  recently  shown, 
even  of  the  bodies  which  make  up  the  solar  sys- 
tem of  the  almost  infinitesimal  atom. 

This  mysterious  attractive  power  that  one  body 
possesses  for  another  is  called  "gravitation," 
and  the  law  which  regulates  the  motion  of  bodies 
when  under  the  spell  of  gravitation  is  the  law  of 
gravitation.  This  law  we  owe  to  Newton's 
genius. 

Newton' *s  Predecessors.  We  can  best  appreciate 
Newton's  momentous  contribution  to  astronomy 
by  casting  a  rapid  glance  over  the  state  of  the 


From  Newton  to  Einstein 


science  prior  to  the  seventeenth  century — that  is, 
prior  to  Newton's  day.  Ptolemy's  conception  of 
the  earth  as  the  center  of  the  universe  held  un- 
disputed sway  throughout  the  middle  ages.  In 
those  days  Ptolemy  was  in  astronomy  what 
Aristotle  was  in  all  other  knowledge:  they  were 
the  gods  who  could  not  but  be  right.  Did  not 
Aristotle  say  that  earth,  air,  fire  and  water  con- 
stituted the  four  elements?  Did  not  Ptolemy 
say  that  the  earth  was  the  center  around  which 
the  sun  revolved?  Why,  then,  question  further? 
Questioning  was  a  sacrilege. 

Copernicus  (1473-1543),  however,  did  ques- 
tion. He  studied  much  and  thought  much.  He 
devoted  his  whole  life  to  the  investigation  of  the 
movements  of  the  heavenly  bodies.  And  he 
came  to  the  conclusion  that  Ptolemy  and  his  fol- 
lowers in  succeeding  ages  had  expounded  views 
which  were  diametrically  opposed  to  the  truth. 
The  sun,  said  Copernicus,  did  not  move  at  all, 
but  the  earth  did;  and  far  from  the  earth  being 
the  center  of  the  universe,  it  was  but  one  of  sev- 
eral planets  revolving  around  the  sun. 

The  influence  of  the  church,  coupled  with  man's 
inclination  to  exalt  his  own  importance,  strongly 
tended  against  the  acceptance  of  such  heterodox 
views.  Among  the  many  hostile  critics  of  the 


From  Newton  to  Einstein 


Copernican  system,  Tycho  Brahe  (1546-1601) 
stands  out  pre-eminently.  This  conscientious 
observer  bitterly  assailed  Copernicus  for  his 
suggestion  that  the  earth  moved,  and  developed 
a  scheme  of  his  own  which  postulated  that  the 
planets  revolved  around  the  sun,  and  planets 
and  sun  in  turn  revolved  around  the  earth. 

The  majority  applauded  Tycho;  a  small,  very 
small  group  of  insurgents  had  faith  in  Copernicus. 
The  illustrious  Galileo  (1564-1642)  belonged  to 
the  minority.  The  telescope  of  his  invention 
unfolded  a  view  of  the  universe  which  belied  the 
assertions  of  the  many,  and  strengthened  his  be- 
lief in  the  Copernican  theory.  "It  (the  Coper- 
nican theory)  explains  to  me  the  cause  of  many 
phenomena  which  under  the  generally  accepted 
theory  are  quite  unintelligible.  I  have  collected 
arguments  for  refuting  the  latter,  but  I  do  not 
venture  to  bring  them  to  publication."  So  wrote 
Galileo  to  his  friend,  Kepler.  "I  do  not  ven- 
ture to  bring  them  to  publication."  How  sig- 
nificant of  the  times — of  any  time,  one  ventures 
to  add. 

Galileo  did  overcome  his  hesitancy  and  pub- 
lished his  views.  They  aroused  a  storm.  "Look 
through  my  telescope,"  he  pleaded.  But  the 
professors  would  not;  neither  would  the  body  of 


- 


From  Newton  to  Einstein 


Inquisitors.  The  Inquisition  condemned  him: 
"The  proposition  that  the  sun  is  in  the  center  of 
the  earth  and  immovable  from  its  place  is  absurd, 
philosophically  false  and  formally  heretical;  be- 
cause it  is  expressly  contrary  to  the  Holy  Scrip- 
tures." And  poor  Galileo  was  made  to  utter 
words  which  were  as  far  removed  *-^m  his 
thoughts  as  his  oppressors'  ideas  were  from  the 
truth:  "I  abjure,  curse  and  detest  the  said 
errors  and  heresies." 

The  truth  will  out.  Others  arose  who  defied 
the  majority  and  the  powerful  Inquisition.  Most 
prominent  of  all  of  these  was  Galileo's  friend, 
Kepler.  t  Though  a  student  of  Tycho,  Kepler 
did  not  hesitate  to  espouse  the  Copernican  sys- 
tem; but  his  adoption  of  it  did  not  mean  unquali- 
fied approval.  Kepler's  criticism  was  particu- 
larly directed  against  the  Copernican  theory  that 
the  planets  revolve  vin  circles.  This  was  bold- 
ness in  the  extreme.  Ever  since  Aristotle's  dis- 
course on  the  circle  as  a  perfect  figure,  it  was 
taken  for  granted  that  motion  in  space  was  cir- 
cular. Nature  is  perfect;  the  circle  is  perfect; 
hence,  if  the  sun  revolves,  it  revolves  in  circles. 
So  strongly  were  men  imbued  with  this  "per- 
fection," that  Copernicus  himself  fell  victim. 
The  sun  no  longer  moved,  but  the  earth  and  the 


From  Newton  to  Einstein 


= 


planets  did,  and  they  moved  in  a  circle.  Rad- 
ical as  Copernicus  was,  a  few  atoms  of  conserv- 
atism remained  with  him  still. 

Not  so  Kepler.  Tycho  had  taught  him  the 
importance  of  careful  observation, — to  such  good 
effect,  that  Kepler  came  to  th^  conclusion  that 
the  revolution  of  the  earth  around  the  sun  takes 
the  form  of  an  ellipse  rather  than  a  circle,  the 
sun  being  stationed  at  one  of  the  foci  of  the  ellipse. 

To  picture  this  ellipse,  we  shall  ask  the  reader 
to  stick  two  pins  a  short  distance  apart  into  a 
piece  of  cardboard,  and  to  place  over  the  pins  a 
loop  of  string.  With  the  point  of  a  pencil  draw 
the  loop  taut.  As  the  pencil  moves  around  the 
two  pins  the  curve  so  produced  will  be  an  ellipse. 
The  positions  of  the  two  pins  represent  the  two 
foci. 

Kepler's  observation  of  the  elliptical  rotation 
of  the  planets  was  the  first  of  three  laws,  quanti- 
tatively expressed,  which  paved  the  way  for 
Newton's  law.  Why  did  the  planets  move  in 
just  this  way?  Kepler  tried  to  answer  this 
also,  but  failed.  It  remained  for  Newton  to 
supply  the  answer  to  this  question. 
.  Newton9 s  Law  of  Gravitation.  The  Great  Plague 
of  1666  drove  Newton  from  Cambridge  to  his 
home  in  Lincolnshire.  There,  according  to  the 


From  Newton  to  Einstein 


celebrated  legend,  the  philosopher  sitting  in  his 
little  garden  one  fine  afternoon,  fell  into  a  deep 
reverie.  This  was  interrupted  by  the  fall  of  an 
apple,  and  the  thinker  turned  his  attention  to 
the  apple  and  its  fall. 

It  must  not  be  supposed  that  Newton  "dis- 
covered" gravity.  Apples  had  been  seen  to  fall 
before  Newton's  time,  and  the  reason  for  their 
return  to  earth  was  correctly  attributed  to  this 
mysterious  force  of  attraction  possessed  by  the 
earth,  to  which  the  name  "gravity"  had  been 
given.  Newton's  great  triumph  consisted  in 
showing  that  this  "gravity,"  which  was  supposed 
to  be  a  peculiar  property  residing  in  the  earth] 
was  a  universal  property  of  matter;  that  it  ap-j' 
plied  to  the  moon  and  the  sun  as  well  as  to  the 
earth;  that,  in  fact,  the  motions  of  the  moon  and 
the  planets  could  be  explained  on  the  basis  of 
gravitation.  But_  his^  supreme^  triumph  was 
to  give,  in  o^^ublinie^genera^ation,  quanti- 
tative expression  teethe  motion^ regulating  heav- 
enTy^bodies. 

Let  us  follow  Newton  in  his  train  of  thought. 
An  apple  falls  from  a  tree  50  yards  high.  It 
would  fall  from  a  tree  500  yards  high.  It  would 
fall  from  the  highest  mountain  top  several  miles 
above  sea  level.  It  would  probably  fall  from  a 


From  Newton  to  Einstein 


- 


height  much  above  the  mountain  top.  Why  not? 
Probably  the  further  up  you  go  the  less  does  the 
earth  attract  the  apple,  but  at  what  distance  does 
this  attraction  stop  entirely? 

The  nearest  body  in  space  to  the  earth  is  the 
moon,  some  240,000  miles  away.  Would  an 
apple  reach  the  earth  if  thrown  from  the  moon? 
But  perhaps  the  moon  itself  has  attractive  power? 
If  so,  since  the  apple  would  be  much  nearer  the 
moon  than  the  earth,  the  probabilities  are  that 
the  apple  would  never  reach  the  earth. 

But  hold!  The  apple  is  not  the  only  object 
that  falls  to  the  ground.  What  is  true  of  the 
apple  is  true  of  all  other  bodies — of  all  matter, 
large  and  small.  Now  there  is  the  moon  itself,  a 
very  large  body.  Does  the  earth  exert  any 
gravitational  pull  on  the  moon?  To  be  sure,  the 
moon  is  many  thousands  of  miles  away,  but  the 
moon  is  a  very  large  body,  and  perhaps  this  size 
is  in  some  way  related  to  the  power  of  attraction? 

But  then  if  the  earth  attracts  the  moon,  why 
does  not  the  moon  fall  to  the  earth? 

A  glance  at  the  accompanying  figure  will  help 
to  answer  this  question.  We  must  remember 
that  the  moon  is  not  stationary,  but  travelling  at 
tremendous  speed — so  much  so,  that  it  circles 
the  entire  earth  every  month.  Now  if  the  earth 


From  Newton  to  Einstein 


were  absent  the  path  of  the  moon  would  be  a 
straight  line,  say  MB.  If,  however,  the  earth 
exerts  attraction,  the  moon  would  be  pulled  in- 

M  B 


ward.  Instead  of  following  the  line  MB  it  would 
follow  the  curved  path  MB'.  And  again,  the 
moon  having  arrived  at  B',  is  prevented  from  fol- 
lowing the  line  E'C,  but  rather  B'C'.  So  that 
the  path  instead  of  being  a  straight  line  tends 
to  become  curved.  From  Kepler's  researches  the 
probabilities  were  that  this  curve  would  assume 
the  shape  of  an  ellipse  rather  than  a  circle. 

The  only  reason,  then,  why  the  moon  does  not 
fall  to  the  earth  is  on  account  of  its  motion.  Were 
it  to  stop  moving  even  for  the  fraction  of  a  second 
it  would  come  straight  down  to  us,  and  probably 
few  would  live  to  tell  the  tale. 


10  From  Newton  to  Einstein 

Newton  reasoned  that  what  keeps  the  moon 
revolving  around  the  earth  is  the  gravitational 
pull  of  the  latter.  The  next  important  step  was 
to  discover  the  law  regulating  this  motion. 
Here  Kepler's  observations  of  the  movements  of 
the  planets  around  the  sun  was  of  inestimable 
value;  for  from  these  Newton  deduced  the 
hypothesis  that  attraction  varies  inversely  as 
the  square  of  the  distance.  Making  use  of  this 
hypothesis,  Newton  calculated  what  the  attractive 
power  possessed  by  the  earth  must  be  in  order 
that  the  moon  may  continue  in  its  path.  He 
next  compared  this  force  with  the  force  exerted 
by  the  earth  in  pulling  the  apple  to  the  ground, 
and  found  the  forces  to  be  identical!  "I  com- 
pared," he  writes,  "the  force  necessary  to  keep 
the  moon  in  her  orb  with  the  force  of  gravity 
at  the  surface  of  the  earth,  and  found  them 
answer  pretty  nearly."  One  and  the  same  force 
pulls  the  moon  and  pulls  the  apple — the  force 
of  gravity.  Further,  the  hypothesis  that  the 
force  of  gravity  varies  inversely  as  the  square  of 
the  distance  had  now  received  experimental  con- 
firmation. 

The  next  step  was  perfectly  clear.  If  the 
moon's  motion  is  controlled  by  the  earth's  gravi- 
tational pull,  why  is  it  not  possible  that  the  earth's 


From  Newton  to  Einstein  11 

motion,  in  turn,  is  controlled  by  the  sun's  gravi- 
tational pull?  that,  in  fact,  not  only  the  earth's 
motion,  but  the  motion  of  all  the  planets  is  reg- 
ulated by  the  same  means? 

Here  again  Kepler's  pioneer  work  was  a  foun- 
dation comparable  to  reinforced  concrete.  Kep- 
ler, as  we  have  seen,  had  shown  that  the  earth 
revolves  around  the  sun  in  the  form  of  an  ellipse, 
one  of  the  foci  of  this  ellipse  being  occupied  by 
the  sun.  \  Newton  now  proved  that  such  an  ellip- 
tic path  was  possible  only  if  the  intensity  of  the 
attractive  force  between  sun  and  planet  varied 
inversely  as  the  square  of  the  distance — the  very 
same  relationship  that  had  been  applied  with 
such  success  in  explaining  the  motion  of  the  moon 
around  the  earth! 

Newton  showed  that  the  moon,  the  sun,  the 
planets — every  body  in  space  conformed  to  this 
law.  The  earth  attracts  the  moon;  but  so  does 
the  moon  the  earth.  If  the  moon  revolves  around 
the  earth  rather  than  the  earth  around  the  moon, 
it  is  because  the  earth  is  a  much  larger  body,  and 
hence  its  gravitational  pull  is  stronger.  The 
same  is  true  of  the  relationship  existing  between 
the  earth  and  the  sun. 

Further  Developments  of  Newton's  Law  of 
Gravitation.  When  we  speak  of  the  earth  attract- 


From  Newton  to  Einstein 


ing  the  moon,  and  the  moon  the  earth,  what  we 
really  mean  is  that  every  one  of  the  myriad  par- 
ticles composing  the  earth  attracts  every  one  of 
the  myriad  particles  composing  the  moon,  and 
vice  versa.  If  in  dealing  with  the  attractive 
forces  existing  between  a  planet  and  its  satellite, 
or  a  planet  and  the  sun,  the  power  exerted  by 
every  one  of  these  myriad  particles  would  have 
to  be  considered  separately,  then  the  mathemat- 
ical task  of  computing  such  forces  might  well 
appear  hopeless.  Newton  was  able  to  present 
the  problem  in  a  very  simple  form  by  pointing 
out  that  in  a  sphere  such  as  the  earth  or  the  moon, 
the  entire  mass  might  be  considered  as  residing 
in  the  center  of  the  sphere.  For  purposes  of  com- 
putation, the  earth  can  be  considered  a  particle, 
with  its  entire  mass  concentrated  at  the  center 
of  the  particle.  This  viewpoint  enabled  Newton 
to  extend  his  law  of  inverse  squares  to  the  re- 
motest bodies  in  the  universe. 

If  this  great  law  of  Newton's  found  such  gen- 
eral application  beyond  our  planet,  it  served  an 
equally  useful  purpose  in  explaining  a  number  of 
puzzling  features  on  this  planet.  The  ebb 
and  flow  of  the  tides  was  one  of  these  puzzles. 
Even  in  ancient  times  it  had  been  noticed  that  a 
full  moon  and  a  high  tide  went  hand  in  hand,  and 


From  Newton  to  Einstein  13 

various  mysterious  powers  were  attributed  to  the 
satellite  and  the  ocean.  .  Newton  pointed  out 
that  the  height  of  the  water  was  a  direct  conse- 
quence of  the  attractive  power  of  the  moon,  and, 
to  a  lesser  extent,  because  further  away,  of  the 
sun. 

One  of  his  first  explanations,  however,  dealt 
with  certain  irregularities  in  the  moon's  motion 
around  the  earth.  If  the  solar  system  would 
consist  of  the  earth  and  moon  alone,  then  the 
path  of  the  moon  would  be  that  of  an  ellipse, 
with  one  of  the  foci  of  this  ellipse  occupied  by 
the  earth.  Unfortunately  for  the  simplicity  of 
the  problem,  there  are  other  bodies  relatively 
near  in  space,  particularly  that  huge  body,  the 
sun.  The  sun  not  only  exerts  its  pull  on  the  earth 
but  also  on  the  moon.  However,  as  the  sun  is 
much  further  away  from  the  moon  than  is  the 
earth,  the  earth's  attraction  for  its  satellite  is 
much  greater,  despite  the  fact  that  the  sun  is 
much  huger  and  weighs  far  more  than  the  earth. 
The  greater  pull  of  the  earth  in  one  direction,  and 
a  lesser  pull  of  the  sun  in  another,  places  the  poor 
moon  between  the  devil  and  the  deep  sea.  The 
situation  gives  rise  to  a  complexity  of  forces,  the 
net  result  of  which  is  that  the  moon's  orbit  is  not 
quite  that  of  an  ellipse.  Newton  was  able  to 


14  From  Newton  to  Einstein 

account  for  all  the  forces  that  come  into  play, 
and  he  proved  that  the  actual  path  of  the  moon 
was  a  direct  consequence  of  the  law  of  inverse 
squares  in  actual  operation. 

The  "Principia"  The  law  of  gravitation, 
embodying  also  laws  of  motion,  which  we  shall 
discuss  presently,  was  first  published  in  New- 
ton's immortal  "Principia"  (1686).  A  selection 
from  the  preface  will  disclose  the  contents  of  the 
booky  and,  incidentally,  the  style  of  the  au- 
thor: "...  We  offer  this  work  as  mathematical 
principles  of  philosophy;  for  all  the  difficulty  in 
philosophy  seems  to  consist  in  this — from  the 
phenomena  of  motions  to  investigate  the  forces  of 
nature,  and  then  from  these  forces  to  demonstrate 
the  other  phenomena;  and  to  this  end  the  gen- 
eral propositions  in  the  first  and  second  book  are 
directed.  In  the  third  book  we  give  an  example 
of  this  in  the  explication  of  the  system  of  the 
world;  for  by  the  propositions  mathematically 
demonstrated  in  the  first  book,  we  there  derive 
from  the  celestial  phenomena  the  forces  of  grav- 
ity with  which  bodies  tend  to  the  sun  and  the 
several  planets.  Then,  from  these  forces,  by 
other  propositions  which  are  also  mathematical, 
we  deduce  the  motions  of  the  planets,  the  comets, 
the  moon  and  the  sea.  I  wish  we  could  derive 


From  Newton  to  Einstein  15 

the  rest  of  the  phenomena  of  nature  by  the  same 
kind  of  reasoning  from  mechanical  principles; 
for  I  am  induced  by  many  reasons  to  suspect 
that  they  may  all  depend  upon  certain  forces  by 
which  the  particles  of  bodies,  by  some  causes 
hitherto  unknown,  are  either  mutually  impelled 
towards  each  other,  and  cohere  in  regular  figures, 
or  are  repelled  and  recede  from  each  other.  ..." 

At  this  point  we  may  state  that  neither  New- 
ton, nor  any  of  Newton's  successors  including 
Einstein,  have  been  able  to  advance  even  a 
plausible  theory  as  to  the  nature  of  this  gravita- 
tional force.  We  know  that  this  force  pulls  a 
stone  to  the  ground;  we  know,  thanks  to  Newton, 
the  laws  regulating  the  motions  due  to  gravity; 
but  what  this  force  we  call  gravity  really  is  we 
do  not  know.  The  mystery  is  as  deep  as  the 
mystery  of  the  origin  of  life. 

"Prof.  Einstein,"  writes  Prof.  Eddington,  "has 
sought,  and  has  not  reached,  any  ultimate  ex- 
planation of  its  [that  is,  gravitation]  cause.  A 
certain  connection  between  the  gravitational  field 
and  the  measurement  of  space  has  been  postulated, 
but  this  throws  light  rather  on  the  nature  of  our 
measurements  than  on  gravitation  itself.  The 
relativity  theory  is  indifferent  to  hypotheses  as 


16  From  Newton  to  Einstein 

to  the  nature  of  gravitation,  just  as  it  is  indiffer- 
ent to  hypotheses  as  to  the  nature  of  light." 

Newton's  Laws  of  Motion.  In  his  Principia 
Newton  begins  with  a  series  of  simple  definitions 
dealing  with  matter  and  force,  and  these  are  fol- 
lowed by  his  three  famous  laws  of  motion.  The 
nature  and  amount  of  the  effort  required  to  start 
a  body  moving,  and  the  conditions  required  to 
keep  a  body  in  motion,  are  included  in  these 
laws.  The  Fundamentals,  mass,  time  and  space, 
are  exhibited  in  their  various  relationships.  Of 
importance  to  us  particularly  is  that  in  these 
laws,  time  and  space  are  considered  as  definite 
entities,  and  as  two  distinct  and  widely  separated 
manifestations.  We  shall  see  that  in  Einstein's 
hands  a  very  close  relationship  between  these 
two  is  brought  about. 

Both  Newton  and  Einstein  were  led  to  their 
theory  of  gravitation  by  profound  studies  of  the 
mathematics  of  motion,  but  as  Newton's  concep- 
tion of  motion  differed  from  Einstein's,  and  as, 
moreover,  important  discoveries  into  the  nature 
of  matter  and  the  relationship  of  motion  to  mat- 
ter were  made  subsequent  to  Newton's  time,  we 
need  not  wonder  that  the  two  theories  show  di- 
vergence; that,  as  we  shall  see,  Newton's  is  prob- 
ably but  an  approximation  of  the  truth.  If  we 


From  Newton  to  Einstein  17 

confine  our  attention  to  our  own  solar  system, 
the  deviation  from  Newton's  law  is,  as  a  rule,  so 
small  as  to  be  negligible. 

Newton's  laws  of  motion  are  really  axioms, 
like  the  axioms  of  Euclid:  they  do  not  admit  of 
direct  proof;  but  there  is  this  difference,  that  the 
axioms  of  Euclid  seem  more  obviously  true. 
For  example,  when  Euclid  informs  us  that 
"things  which  are  equal  to  the  same  thing  are 
equal  to  one  another,"  we  have  no  hesitation  in 
accepting  this  statement,  for  it  seems  so  self- 
evident.  When,  however,  we  are  told  by  New- 
ton that  "  the  alteration  of  motion  is  ever  propor- 
tional to  the  motive  force  impressed,"  we  are  at 
first  somewhat  bewildered  with  the  phraseology, 
and  then,  even  when  that  has  been  mastered,  the 
readiness  with  which  we  respond  will  probably 
depend  upon  the  amount  of  scientific  training  we 
have  received. 

"Every  body  continues  in  its  state  of  rest  or  of 
uniform  motion  in  a  straight  line,  unless  it  is 
compelled  to  change  that  state  by  forces  impressed 
thereon."  So  runs  Newton's  first  law  of  motion. 
A  body  does  not  move  unless  something  causes  it 
to  move;  to  make  the  body  move  you  must 
overcome  the  inertia  of  the  body.  On  the  other 
hand,  if  a  body  is  moving,  it  tends  to  continue 


18  From  Newton  to  Einstein 

moving,  as  witness  our  forward  movement  when 
the  train  is  brought  to  a  standstill.  It  may  be 
asked,  why  does  not  a  bullet  continue  moving 
indefinitely  once  it  has  left  the  barrel  of  the  gun? 
Because  of  the  resistance  of  the  air  which  it  has 
to  overcome;  and  the  path  of  the  bullet  is  not 
straight  because  gravity  acts  on  it  and  tends  to 
pull  it  downwards. 

We  have  no  definite  means  of  proving  that  a 
body  once  set  in  motion  would  continue  moving, 
for  an  indefinite  time,  and  along  a  straight  line. 
What  Newton  meant  was  that  a  body  would 
continue  moving  provided  no  external  force 
acted  on  it;  but  in  actual  practise  such  a  con- 
dition is  unknown. 

Newton's  first  law  defines  force  as  that  action 
necessary  to  change  a  state  of  rest  or  of  uniform 
motion,  and  tells  us  that  force  alone  changes  the 
motion  of  a  body.  His  second  law  deals  with 
the  relation  of  the  force  applied  and  the  resulting 
change  of  motion  of  the  body;  that  is,  it  shows  us 
how  force  may  be  measured.  "The  alteration 
of  motion  is  ever  proportional  to  the  motive  force 
impressed,  and  is  made  in  the  direction  of  the 
right  line  in  which  that  force  is  impressed." 

Newton's  third  law  runs — -"To  every  action 
there  is  always  opposed  an  equal  reaction."  The 


From  Newton  to  Einstein  19 

very  fact  that  you  have  to  use  force  means  that 
you  have  to  overcome  something  of  an  opposite 
nature.  The  forward  pull  of  a  horse  towing  a 
boat  equals  the  backward  pull  of  the  tow-rope 
connecting  boat  and  horse.  "Many  people," 
says  Prof.  Watson,  "find  a  difficulty  in  accepting 
this  statement  .  .  .  since  they  think  that  if  the 
force  exerted  by  the  horse  on  the  rope  were  not  a 
little  greater  than  the  backward  force  exerted  by 
the  rope  on  the  horse,  the  boat  would  not  progress. 
In  this  case  we  must,  however,  remember  that, 
as  far  as  their  relative  positions  are  concerned, 
the  horse  and  the  boat  are  at  rest,  and  form  a 
single  body,  and  the  action  and  reaction  between 
them,  due  to  the  tension  on  the  rope,  must  be 
equal  and  opposite,  for  otherwise  there  would  be 
relative  motion,  one  with  respect  to  the  other." 

It  may  well  be  asked,  what  bearing  have  these 
laws  of  Newton  on  the  question  of  time  and  space? 
Simply  this,  that  to  measure  force  the  factors 
necessary  are  the  masses  of  the  bodies  concerned, 
the  time  involved  and  the  space  covered;  and 
Newton's  equations  for  measuring  forces  assume 
time  and  space  to  be  quite  independent  of  one 
another.  As  we  shall  see,  this  is  in  striking 
contrast  to  Einstein's  view. 

Newton's  Researches  on  Light.     In  1665,  when 


20  From  Newton  to  Einstein 


- 


but  23  years  old,  Newton  invented  the  binomial 
theorem  and  the  infinitesimal  calculus,  two 
phases  of  pure  mathematics  which  have  been  the 
cause  of  many  a  sleepless  night  to  college  fresh- 
men. Had  Newton  done  nothing  else  his  fame 
would  have  been  secure.  But  we  have  already 
glanced  at  his  law  of  inverse  squares  and  the  law 
of  gravitation.  We  now  have  to  turn  to  some  of 
Newton's  contributions  to  optics,  because  here 
more  than  elsewhere  we  shall  find  the  starting 
point  to  a  series  of  researches  which  have  cul- 
minated so  brilliantly  in  the  work  of  Einstein. 

Newton  turned  his  attention  to  optics  in  1666 
when  he  proved  that  the  light  from  the  sun,  which 
appears  white  to  us,  is  in  reality  a  mixture  of  all 
the  colors  of  the  rainbow.  This  he  showed  by 
placing  a  prism  between  the  ray  of  light  and  a 
screen.  A  spectrum  showing  all  the  colors  from 
red  to  violet  appeared  on  the  screen. 

Another  notable  achievement  of  his  was  the 
design  of  a  telescope  which  brought  objects  to  a 
sharp  focus  and  prevented  the  blurring  effects 
which  had  occasioned  so  much  annoyance  to 
Newton  and  his  predecessors  in  all  their  astronom- 
ical observations. 

These  and  other  discoveries  of  very  great  in- 
terest were  brought  together  in  a  volume  on  optics 


From  Newton  to  Einstein  21 

which  Newton  published  in  1704.  Our  particular 
concern  here  is  to  examine  the  views  advanced 
by  him  as  to  the  nature  of  light. 

That  the  nature  of  light  should  have  been  a 
subject  for  speculation  even  to  the  ancients  need 
not  surprise  us.  If  other  senses,  as  touch,  for 
example,  convey  impressions  of  objects,  it  is 
true  to  say  that  the  sense  of  sight  conveys  the 
most  complete  impression.  Oiir  conception  of 
the  external  world  is  largely  based  upon  the  sense 
of  sight;  particularly  so  when  we  deal  with  ob- 
jects beyond  our  reach.  In  astronomy,  there- 
fore, a  study  of  the  properties  of  light  is 
indispensable.* 

But  what  is  this  light?  We  open  our  eyes  and 
we  see;  we  close  our  eyes  and  we  fail  to  see.  At 
night  in  a  da.'k  room  we  may  have  our  eyes  open 
and  yet  we  do  not  see;  light,  then,  must  be 
absent.  Evidently,  light  does  not  wholly  depend 
upon  whether  our  eyes  are  open  or  closed.  This 
much  is  certain:  the  eye  functions  and  some- 
thing else  functions.  What  is  this  "something 
else"? 

Strangely  enough,  Plato  and  Aristotle  re- 
garded light  as  a  property  of  the  eye  and  the  eye 

*  See  Note  1  at  the  end  of  the  volume. 


From  Newton  to  Einstein 


alone.  Out  of  the  eye  tentacles  were  shot  which 
intercepted  the  object  and  so  illuminated  it. 
From  what  has  already  been  said,  such  a  view 
seems  highly  unlikely.  Far  more  consistent 
with  their  philosophy  in  other  directions  would 
have  been  the  theory  that  light  has  its  source  in 
the  object  and  not  in  the  eye,  and  travels  from 
object  to  eye  rather  than  the  reverse.  How  little 
substance  the  Aristotelian  contribution  possesses 
is  immediately  seen  when  we  refer  to  the  art  of 
photography.  Here  light  rays  produce  effects 
which  are  independent  of  any  property  of  the 
eye.  The  blind  man  may  click  the  camera  and 
produce  the  impression  on  the  plate. 

Newton,  of  course,  could  have  fallen  into  no 
such  error  as  did  Plato  and  Aristotle.  The 
source  of  light  to  him  was  the  luminous  body. 
Such  a  body  had  the  power  of  emitting  minute 
particles  at  great  speed,  and  these  when  coming  in 
contact  with  the  retina  produce  the  sensation  of 
sight. 

This  emission  or  corpuscular  theory  of  Newton's 
was  combated  very  strongly  by  his  illustrious 
Dutch  contemporary,  Huyghens,  who  maintained 
that  light  was  a  wave  phenomenon,  the  dis- 
turbance starting  at  the  luminous  body  and 


From  Newton  to  Einstein  23 

spreading  out  in  all  directions.  The  wave  mo- 
tions of  the  sea  offer  a  certain  analogy. 

Newton's  strongest  objection  to  Huyghens' 
wave  theory  was  that  it  seemed  to  offer  no  satis- 
factory explanation  as  to  why  light  travelled  in 
straight  lines.  He  says:  "To  me  the  funda- 
mental supposition  itself  seems  impossible,  namely 
that  the  waves  or  vibrations  of  any  fluid  can, 
like  the  rays  of  light,  be  propagated  in  straight 
lines,  without  a  continual  and  very  extravagant 
bending  and  spreading  every  way  into  the 
quiescent  medium,  where  they  are  terminated  by 
it.  I  mistake  if  there  be  not  both  experiment 
and  demonstration  to  the  contrary." 

In  the  corpuscular  theory  the  particles  emitted 
by  the  luminous  body  were  supposed  to  travel  in 
straight  lines.  In  empty  space  the  particles 
travelled  in  straight  lines  and  spread  in  all 
directions.  To  explain  how  light  could  traverse 
some  types  of  matter — liquids,  for  example — 
Newton  supposed  tEat  .>  these  light  particles 
travelled  in  the  spaces  [between  the  molecules 
of  the  liquid. 

Newton's  objection  to  the  wave  theory  was  not 
answered  very  convincingly  by  Huyghens.  To- 
day we  know  that  light  waves  of  high  frequency 
tend  to  travel  in  straight  lines,  but  may  be  pre- 


From  Newton  to  Einstein 


- 


vented  from  doing  so  by  gravitational  forces  of 
bodies  near  its  path.  But  this  is  Einstein's 
discovery. 

A  very  famous  experiment  by  Foucault  in  1853 
proved  beyond  the  shadow  of  a  doubt  that 
Newton's  corpuscular  theory  was  untenable. 
According  to  Newton's  theory,  the  velocity 
of  light  must  be  greater  in  a  denser  medium 
(such  as  water)  than  in  a  lighter  one  (such  as 
air).  According  to  the  wave  theory  the  reverse 
is  true.  Foucault  showed  that  light  does  travel 
more  slowly  in  water  than  in  air.  The  facts 
were  against  Newton  and  in  favor  of  Huyghens; 
and  where  facts  and  theory  clash  there  is  but 
one  thing  to  do:  discard  the  theory. 

Some  Facts  about  Newton.  Newton  was  a 
Cambridge  man,  and  Newton  made  Cambridge 
famous  as  a  mathematical  center.  Since  New- 
ton's day  Cambridge  has  boasted  of  a  Clerk  Max- 
well and  a  Rayleigh,  and  her  Larmor,  her  J.  J. 
Thomson  and  her  Rutherford  are  still  with  us. 
Newton  entered  Trinity  College  when  he  was  18 
and  soon  threw  himself  into  higher  mathematics. 
In  1669,  when  but  27  years  old,  he  became 
professor  of  mathematics  at  Cambridge,  and 
later  represented  that  seat  of  learning  in  Parlia- 
ment. When  his  friend  Montague  became  Chan- 


From  Newton  to  Einstein  25 

cellor  of  the  Exchequer,  Newton  was  offered,  and 
accepted,  the  lucrative  position  of  Master  of  the 
Mint.  As  president  of  the  Royal  Society  Newton 
was  occasionally  brought  in  contact  with  Queen 
Anne.  She  held  Newton  in  high  esteem,  and  in 
1705  she  conferred  the  honor  of  knighthood  on 
him.  He  died  in  1727. 

"I  do  not  know,"  wrote  Newton,  "what  I  may 
appear  to  the  world,  but,  to  myself,  I  seem  to 
have  been  only  like  a  boy  playing  on  the  sea- 
shore, and  directing  myself  in  now  and  then 
finding  a  smoother  pebble  or  a  prettier  shell  than 
ordinary,  whilst  the  great  ocean  of  truth  lay  all 
undiscovered  before  me." 

Such  was  the  modesty  of  one  whom  many 
regard  as  the  greatest  intellect  of  all  ages. 

REFERENCES 

An  excellent  account  of  Newton  may  be  found 
in  Sir  R.  S.  Ball's  Great  Astronomers  (Sir  Isaac 
Pitman  and  Sons,  Ltd.,  London).  Sedgewick 
and  Tyler's  A  Short  History  of  Science  (Mac- 
millan,  1918)  and  Cajori's  A  History  of  Mathe- 
matics (Macmillan,  1917)  may  also  be  con- 
sulted to  advantage.  The  standard  biography  is 
that  by  Brewster. 


II 

THE  ETHER  AND  ITS  CONSEQUENCES 

JJUYGHENS'  wave  theory  of  light,  now 
so  generally  accepted,  loses  its  entire 
significance  if  a  medium  for  the 
propagation  of  these  waves  is  left  out 
of  consideration.  This  medium  we  call  the  ether.* 
Huyghens'  reasoning  may  be  illustrated  in  some 
such  way  as  this :  If  a  body  moves  a  force  pushes 
or  pulls  it.  That  force  itself  is  exemplified  in 
some  kind  of  matter — say  a  horse.  The  horse 
in  pulling  a  cart  is  attached  to  the  cart.  The 
horse  in  pulling  a  boat  may  not  be  attached  to 
the  boat  directly  but  to  a  rope,  which  in  turn  is 
attached  to  the  boat.  In  common  cases  where 
one  piece  of  matter  affects  another,  there  is  some 
direct  contact,  some  go-between. 

But  cases  are  known  where  matter  affects 
matter  without  affording  us  any  evidence  of  con- 
tact. Take  the  case  of  a  magnet's  attraction  for  a 
piece  of  iron.  Where  is  the  rope  that  pulls  the 
iron  towards  the  magnet?  Perhaps  you  think 
the  attraction  due  to  the  air  in  between  the  mag- 

*  See  Note  2. 

27 


28  From  Newton  to  Einstein 

net  and  iron?  But  removing  the  air  does  not 
stop  the  attraction.  Yet  how  can  we  conceive 
of  the  iron  being  drawn  to  the  magnet  unless  there 
is  some  go-between?  some  medium  not  readily 
perceptible  to  the  senses  perhaps,  and  therefore 
not  strictly  a  form  of  matter? 

If  we  can  but  picture  some  such  medium  we  can 
imagine  our  magnet  giving  rise  to  vibrations  in 
this  medium  which  are  carried  to  the  iron.  The 
magnet  may  give  rise  to  a  disturbance  in  that 
portion  of  the  medium  nearest  to  it;  then  this 
portion  hands  over  the  disturbance  to  its  neigh- 
bor, the  next  portion  of  the  medium;  and  so  on, 
until  the  disturbance  reaches  the  iron.  You 
see,  we  are  satisfying  our  sense-perception  by 
arguing  in  favor  of  action  by  actual  contact 
rather  than  some  vague  action  at  a  distance; 
the  go-between  instead  of  being  a  rope  is  the 
medium  called  the  ether. 

Foucault's  experiment  completely  shattered  the 
corpuscular  theory  of  light,  and  for  want  of  any 
other  more  plausible  alternative,  we  are  thrown 
back  on  Huyghens'  wave  theory.  It  will  presently 
appear  that  this  wave  theory  has  elements  in  it 
which  make  it  an  excellent  alternative.  In  the 
meantime,  if  light  is  to  be  considered  as  a  wave 
motion,  then  the  query  immediately  arises,  what 


From  Newton  to  Einstein  29 

is  the  medium  through  which  these  waves  are 
propagated?  If  water  is  the  medium  for  the 
waves  of  the  sea,  what  is  the  medium  for  the 
waves  of  light?  Again  we  answer,  the  medium 
is  the  ether. 

What  Is  This  "Ether"?  Balloonists  find  con- 
ditions more  and  more  uncomfortable  the  higher 
they  ascend,  for  the  density  of  the  air  (and  there- 
fore the  amount  of  oxygen  in  a  given  volume  of 
air)  becomes  less  and  less.  Meteorologists  have 
calculated  that  traces  of  the  air  we  breathe  may 
reach  a  height  of  some  200  miles.  But  what  is 
beyond?  Nothing  but  the  ether,  it  is  claimed. 
Light  from  the  sun  and  stars  reaches  us  via  the 
ether. 

But  what  is  this  ether?  We  cannot  handle  it. 
We  cannot  see  it.  It  fails  to  fall  within  the  scope 
of  any  of  our  senses,  for  every  attempt  to  show  its 
presence  has  failed.  It  is  spirit-like  in  the  pop- 
ular sense.  It  is  Lodge's  medium  for  the  souls 
of  the  departed. 

Helmholtz  and  Kelvin  tried  to  arrive  at  some 
properties  of  this  hypothetical  substance  from  a 
careful  study  of  the  manner  in  which  waves  were 
propagated  through  this  ether.  If,  as  the  wave 
theory  teaches  us,  the  ether  can  be  set  in  motion, 
then  according  to  laws  of  mechanics,  the  ether 


30  From  Newton  to  Einstein 

has  mass.  If  so  it  is  smaller  in  amount  than 
anything  which  can  be  detected  with  our  most 
accurate  balance.  Further — and  this  is  a  diffi- 
culty not  easily  explained — if  this  ether  has  any 
mass,  why  does  it  offer  no  detectable  resistance 
to  the  velocity  of  the  planets  in  it?  Why  is  not 
the  velocity  of  the  planets  reduced  in  time,  just 
as  the  velocity  of  a  rifle  bullet  decreases  owing 
to  the  resistance  of  the  air? 

Lodge,  in  arguing  in  favor  of  an  ether,  holds 
that  its  presence  cannot  be  detected  because  it 
pervades  all  space  and  all  matter.  His  favorite 
analogy  is  to  point  out  the  extreme  unlikelihood 
of  a  deep-sea  fish  discovering  the  presence  of  the 
water  with  which  it  is  surrounded  on  all  sides; — 
all  of  which  tells  us  nothing  about  the  ether,  but 
does  try  to  tell  us  why  we  cannot  detect  it.* 

In  short,  answering  the  query  at  the  head  of 
this  paragraph,  we  may  say  that  we  do  not  know. 

Waves  Set  up  in  This  Ether.  The  waves  are 
not  all  of  the  same  length.  Those  that  produce 
the  sensation  of  sight  are  not  the  smallest  waves 
known,  yet  their  length  is  so  small  that  it  would 
take  anywhere  from  one  to  two  million  of  them  to 
cover  a  yard.  Curiously  enough,  our  eye  is  not 
sensitive  to  wave  lengths  beyond  either  side  of 
these  limits;  yet  much  smaller,  and  much  larger 

*  See  Note  3. 


From  Newton  to  Einstein  81 

waves  are  known.  The  smallest  are  the  famous 
X-rays,  which  are  scarcely  one  ten-thousandth 
the  size  of  light  waves.  Waves  which  have  a 
powerful  chemical  action — those  which  act  on  a 
photographic  plate,  for  example — are  longer 
than  X-rays,  yet  smaller  than  light  waves. 
Waves  larger  than  light  waves  are  those  which 
produce  the  sensation  of  heat,  and  those  used  in 
wireless  telegraphy.  The  latter  may  reach  the 
enormous  length  of  5,000  yards.  X-ray,  actinic, 
or  chemically  active  ray,  light  ray,  heat  ray, 
wireless  ray — they  differ  in  size,  yet  they  all  have 
this  in  common:  they  travel  with  the  same  speed 
(186,000  miles  per  second). 

The  Electromagnetic  Theory  of  Light.  Power- 
ful support  to  the  conception  that  space  is  per- 
vaded by  ether  was  given  when  Maxwell  dis- 
covered light  to  be  an  electro-magnetic  phe- 
nomenon. From  purely  theoretical  considera- 
tions this  gifted  English  physicist  was  led  to  the 
view  that  waves  could  be  set  up  as  a  result  of 
electrical  disturbances.  He  proved  that  such 
waves  would  travel  with  the  same  velocity  as  light 
waves.  As  air  is  not  needed  to  transmit  elec- 
trical phenomena — for  you  can  pump  all  air  out 
of  a  system  and  produce  a  vacuum,  and  electrical 
phenomena  will  continue — Maxwell  was  forced  to 


32  From  Newton  to  Einstein 

the  conclusion  that  the  waves  set  up  by  electrical 
disturbances  and  transmitted  with  the  same  veloc- 
ity as  light,  were  enabled  to  do  so  with  the  help 
of  the  same  medium  as  light,  namely,  the  ether. 

It  was  now  but  a  step  for  Maxwell  to  formulate 
the  theory  that  light  itself  is  nothing  but  an  elec- 
trical phenomenon,  the  sensation  of  light  being 
due  to  the  passage  of  electric  waves  through  the 
ether.  This  theory  met  with  considerable  oppo- 
sition at  first.  Physicists  had  been  brought  up 
in  a  school  which  had  taught  that  light  and  elec- 
tricity were  two  entirely  unrelated  phenomena, 
and  it  was  difficult  for  them  to  loosen  the  shackles 
that  bound  them  to  the  older  school.  But  two 
startling  discoveries  helped  to  fasten  attention 
upon  Maxwell's  theory.  One  was  an  experi- 
mental confirmation  of  Maxwell's  theoretical 
deduction.  Hertz,  a  pupil  of  Helmholtz,  showed 
how  the  discharge  from  a  Ley  den  jar  set  up 
oscillations,  which  in  turn  gave  rise  to  waves  in 
the  ether,  comparable,  in  so  far  as  velocity  is 
concerned,  to  light  waves,  but  differing  from  the 
latter  in  wave  length,  the  Hertzian  waves  being 
much  longer.  At  a  later  date  these  waves  were 
further  investigated  by  Marconi,  with  the  result 
that  wireless  messages  soon  began  to  be  flashed 
from  one  place  to  another. 


From  Newton  to  Einstein  33 

Just  as  there  is  a  close  connection  between  light 
and  electricity,  so  there  is  between  light  and 
magnetism.  The  first  to  point  out  such  a  rela- 
tionship was  the  illustrious  Michael  Faraday,  but 
we  owe  to  Zeeman  the  most  extensive  investiga- 
tions in  this  field. 

If  we  throw  some  common  salt  into  a  flame,  and, 
with  the  help  of  a  spectroscope,  examine  the 
spectrum  produced,  we  are  struck  by  two  bright 
lines  which  stand  out  very  prominently.  These 
lines,  yellow  in  color,  are  known  as  the  D-lines 
and  serve  to  identify  even  minute  traces  of  sodium. 
What  is  true  of  sodium  is  true  of  other  elements: 
they  all  produce  very  characteristic  spectra. 
Now  Zeeman  found  that  if  the  flame  is  placed 
between  a  powerful  magnet,  and  then  some  com- 
mon salt  thrown  into  the  flame,  the  two  yellow 
lines  give  place  to  ten  yellow  lines.  Such  is  one  of 
the  results  of  the  effect  of  a  magnetic  field  on 
light. 

The  Electron.  The  "Zeeman  effect"  led  to 
several  theories  regarding  its  nature.  The  most 
successful  of  these  was  one  proposed  by  Larmor 
and  more  fully  treated  by  Lorentz.  It  has 
already  been  pointed  out  that  the  only  difference 
between  wireless  and  light  waves  is  that  the 
former  are  much  "longer,"  and,  we  may  now  add, 


34  From  Newton  to  Einstein 

their  vibrations  are  much  slower.  Light  and 
wireless  waves  bear  a  relationship  to  one  another 
comparable  to  the  relationship  born  by  high  and 
low-pitched  sounds.  To  produce  wireless  waves 
we  allow  a  charge  of  electricity  to  oscillate  to  and 
fro.  These  oscillations,  or  oscillating  charges, 
are  the  cause  of  such  waves.  What  charges  give 
rise  to  light  waves?  Lorentz,  from  a  study  of  the 
Zeeman  effect,  ascribed  them  to  minute  particles 
of  matter,  smaller  than  the  chemical  atom,  to 
which  the  name  "electron"  was  given. 

The  unit  of  electricity  is  the  electron.  Elec- 
trons in  motion  give  rise  to  electricity,  and  elec- 
trons in  vibration,  to  light.  The  Zeeman  effect 
gave  Lorentz  enough  data  to  calculate  the  mass 
of  such  electrons.  He  then  showed  that  these 
electrons  in  a  magnetic  field  would  be  disturbed 
by  precisely  the  amount  to  which  Zeeman's  obser- 
vations pointed.  In  other  words,  the  assumption 
of  the  electron  fitted  in  most  admirably  with 
Zeeman's  experiments  on  magnetism  and  light. 

In  the  meantime,  a  study  of  the  discharge  of 
electricity  through  gases,  and,  later,  the  discovery 
of  radium,  led,  among  other  things,  to  a  study  of 
beta  or  cathode  rays — negatively  charged  par- 
ticles of  electricity.  Through  a  series  of  strik- 
ingly original  experiments  J.  J.  Thomson  ascer- 


From  Newton  to  Einstein  35 

tained  the  mass  of  such  particles  or  corpuscles, 
and  then  the  very  striking  fact  was  brought  out 
that  Thomson's  corpuscle  weighed  the  same  as 
Lorentz's  electron.  The  electron  was  not  merely 
the  unit  of  electricity  but  the  smallest  particle 
of  matter. 

The  Nature  of  Matter.  All  matter  is  made  up 
of  some  eighty-odd  elements.  Oxygen,  copper, 
lead  are  examples  of  such  elements.  Each  element 
in  turn  consists  of  an  innumerable  number  of 
atoms,  of  a  size  so  small,  that  300  million  of  them 
could  be  placed  alongside  of  one  another  without 
their  total  length  exceeding  one  inch. 

John  Dalton  more  than  a  hundred  years  ago 
postulated  a  theory,  now  known  as  the  atomic 
theory,  to  explain  one  of  the  fundamental  laws  in 
chemistry.  This  theory  started  out  with  an  old  ' 
Greek  assumption  that  matter  cannot  be  divided 
indefinitely,  but  that,  by  continued  subdivision, 
a  point  would  be  reached  beyond  which  no  further 
breaking  up  would  be  possible.  The  particles 
at  this  stage  Dalton  called  atoms. 

Dalton's  atomic  hypothesis  became  one  of  the 
pillars  upon  which  the  whole  superstructure  of 
chemistry  rested,  and  this  because  it  explained  a 
number  of  perplexing  difficulties  so  much  more 
satisfactorily  than  any  other  hypothesis. 


. 


36  From  Newton  to  Einstein 

For  nearly  a  century  Dalton  stood  as  firm  as  a 
rock.  But  early  in  the  nineties  some  epoch- 
making  experiments  on  the  discharge  of  elec- 
tricity through  gases  were  begun  by  a  group  of 
physicists,  particularly  Crookes,  Rutherford,  Le- 
nard,  Roentgen,  Becquerel,  and,  above  all,  J.  J. 
Thomson,  which  pointed  very  clearly  to  the  fact 
that  the  atoms  are  not  the  smallest  particles  of 
matter  at  all;  that,  in  fact,  they  could  be  broken 
up  into  electrons,  of  a  diameter  one  one-hundred- 
thousandth  that  of  an  atom. 

It  remained  for  the  illustrious  Madame  Curie 
to  confirm  this  beyond  all  doubt  by  her  isolation 
of  radium.  Here,  as  Madame  Curie  showed,  was 
an  element  whose  atoms  were  actually  breaking 
up  under  one's  very  eyes,  so  to  speak. 

So  far  have  we  advanced  since  Dalton's  day, 
— -that,Dalton's  unit,  the  atom,  is  now  pictured  as  a 
complex  particle  patterned  after  our  solar  system, 
with  a  nucleus  of  positive  electricity  in  the  center, 
and  particles  of  negative  electricity,  or  electrons, 
surrounding  the  nucleus. 

All  this  leads  to  one  inevitable  conclusion: 
matter  is  electrical  in  nature.  But  now  if  matter 
and  light  have  the  same  origin,  and  matter  is  sub- 
ject to  gravitation,  why  not  light  also?  So  rea- 
soned Einstein. 


From  Newton  to  Einstein  37 

Summary.  Newton's  studies  of  matter  in 
motion  led  to  his  theory  of  gravitation,  and,  in- 
cidentally, to  his  conception  of  time  and  space 
as  definite  entities.  As  we  shall  see,  Einstein  in 
his  theory  of  gravitation  based  it  upon  discoveries 
belonging  to  the  post-Newtonian  period.  One  of 
these  is  Minkowski's  theory  of  time  and  space  as 
one  and  inseparable.  This  theory  we  shall  dis- 
cuss at  some  length  in  the  next  chapter. 

Other  important  discoveries  which  led  up  to 
Einstein's  work  are  the  researches  which  cul- 
minated in  the  electron  theory  of  matter.  The 
origin  of  this  theory  may  be  traced  to  studies 
dealing  with  the  nature  of  light. 

Here  again  Newton  appears  as  a  pioneer.  New- 
ton's corpuscular  theory,  however,  proved  wholly 
untenable  when  Foucault  showed  that  the  velocity 
of  light  in  water  is  less  than  in  air,  which  is  the 
very  reverse  of  what  the  corpuscular  theory  de- 
mands, but  which  does  agree  with  Huyghens'  wave 
theory. 

But  Huyghens'  wave  theory  postulated  some 
medium  in  which  the  waves  can  act.  To  this 
medium  the  name  "ether"  was  given.  However, 
all  attempts  to  show  the  presence  of  such  an  ether 
failed.  Naturally  enough,  some  began  to  doubt 
the  existence  of  an  ether  altogether. 


38  From  Newton  to  Einstein 

Huyghens'  wave  theory  received  a  new  lease  of 
life  with  Maxwell's  discovery  that  light  is  an 
electromagnetic  phenomenon;  that  the  waves 
set  up  by  a  source  of  light  were  comparable  to 
waves  set  up  by  an  electrical  disturbance. 

Zeeman  next  showed  that  magnetism  was  also, 
closely  related  to  light. 

A  study  of  Zeeman's  experiments  led  Lorentz 
to  the  conclusion  that  electrical  phenomena  are 
due  to  the  motion  of  charged  particles  called 
"electrons,"  and  that  the  vibrations  of  these  elec- 
trons give  rise  to  light. 

The  conception  of  the  electron  as  the  very  fun- 
damental of  matter  was  arrived  at  in  an  entirely 
different  way:  from  studies  dealing  with  the  dis- 
charge of  electricity  through  gases  and  the 
breaking  up  of  the  atoms  of  radium. 

If  matter  and  light  have  the  same  origin,  and  if 
matter  is  subject  to  gravitation,  why  not  light 
also? 

REFERENCES 

For  the  general  subject  of  light  the  reader  must 
be  referred  to  a  rather  technical  work,  but  one  of 
the  best  in  the  English  language:  Edwin  Edser, 
Light  for  Students  (Macmillan,  1907). 

The  nature  of  matter  and  electricity  is  excel- 


From  Newton  to  Einstein  39 

lently  discussed  in  several  books  of  a  popular 
variety.  The  very  best  and  most  complete  of 
its  kind  that  has  come  to  the  author's  attention 
is  Comstock  and  Troland's  The  Nature  of  Matter 
and  Electricity  (D.  Van  Nostrand  Co.,  1919).  Two 
other  very  readable  books  are  Soddy's  Matter 
and  Energy  (Henry  Holt  and  Co.)  and  Crehore's 
The  Mystery  of  Matter  and  Energy  (D.  Van  Nos- 
trand Co.,  1917). 


C.  Wide  World 


ALBERT  EINSTEIN 


Ill 

EINSTEIN 

J HIS  is  the  most  important  result 
obtained  in  connection  with  the 
theory  of  gravitation  since  Newton's 
day.  Einstein's  reasoning  is  the 
result  of  one  of  the  highest  achievements  of 
human  thought." 

These  words  were  uttered  by  Sir  J.  J.  Thomson, 
the  president  of  the  Royal  Society,  at  a  meeting 
of  that  body  held  on  November  6,  1919,  to  discuss 
the  results  of  the  Eclipse  Expedition. 

Einstein  another  Newton — and  this  from  the 
lips  of  J.  J.  Thomson,  England's  most  illustrious 
physicist!  If  ever  man  weighed  words  carefully 
it  is  this  Cambridge  professor,  whose  own  re- 
searches have  assured  him  immortality  for  all 
time. 

What  has  this  Albert  Einstein  done  to  merit 
such  extraordinary  praise?  With  the  world  in 
turmoil,  with  classes  and  races  in  a  death  struggle, 
with  millions  suffering  and  starving,  why  do  we 
find  time  to  turn  our  attention  to  this  Jew? 
41 


42  From  Newton  to  Einstein 

His  ideas  have  no  bearing  on  Europe's  calamity. 
They  will  not  add  one  bushel  of  wheat  to  starving 
populations. 

The  answer  is  not  hard  to  find.  Men  come  and 
men  go,  but  the  mystery  of  the  universe  remains. 
It  is  Einstein's  glory  to  have  given  us  a  deeper 
insight  into  the  universe.  Our  scientists  are 
Huxley's  agnostics:  they  do  not  deny  activities 
beyond  our  planet;  they  merely  center  their 
attention  on  the  knowable  on  this  earth.  Our 
philosophers,  on  the  other  hand,  go  far  afield. 
Some  of  them  soar  so  high  that,  like  one  poet's 
opinion  of  Shelley,  the  bubble  bursts.  Einstein, 
using  the  tools  of  the  scientist — the  experimental- 
ist— builded  a  skyscraper  which  ultimately 
reached  the  philosophical  school.  His  r61e  is  the 
r61e  of  alcohol  in  causing  water  and  ether  (the 
anaesthetic)  to  mix.  Ether  and  water  will  mix  no 
better  than  oil  and  water,  without  the  presence  of 
alcohol;  in  its  presence  a  uniform  mixture  is 
obtained. 

The  Object  of  the  Eclipse  Expedition.  Einstein 
prophesied  that  a  ray  of  light  passing  near  the 
sun  would  be  pulled  out  of  its  course,  due  to  the 
action  of  gravity.  He  went  even  further.  He 
predicted  how  much  out  of  its  course<the  ray 
would  be  deflected.  This  prediction  was  based 


From  Newton  to  Einstein  43 

on  a  theory  of  gravitation  which  Einstein  had 
developed  in  great  mathematical  detail.  The 
object  of  the  British  Eclipse  Expedition  was  either 
to  prove  or  disprove  Einstein's  assumption. 

The  Result  of  the  Expedition.  Einstein's  pro- 
phecy was  fulfilled  almost  to  the  letter. 

The  Significance  of  the  Result.  Since  Einstein's 
theory  of  gravitation  is  intimately  associated  with 
certain  revolutionary  ideas  concerning  time  and 
space,  and,  therefore,  with  Fundamentals  of  the 
Universe,  the  net  result  of  the  expedition  was  to 
strengthen  our  belief  in  the  validity  of  his  new 
view  of  the  universe. 

It  is  our  intention  in  the  following  pages  to  dis- 
cuss the  expedition  and  the  larger  aspects  of 
Einstein's  theory  that  follow  from  it.  But  before 
we  do  so  we  must  have  a  clear  idea  of  our  solar 
system. 

Our  Solar  System.  In  the  center  of  our  system 
is  the  sun,  a  flaming  mass  of  fire,  much  bigger  than 
our  own  earth,  and  very,  very  far  away.  The 
sun  has  its  family  of  eight  planets — of  which  the 
earth  is  one — which  travel  around  the  sun;  and 
around  some  of  the  planets  there  travel  satel- 
lites, or  moons.  The  earth  has  such  a  satellite, 
the  moon. 

Now  we  have  good  reasons  for  believing  that 


44  From  Newton  to  Einstein 

every  star  which  twinkles  in  the  sky  is  a  sun  com- 
parable to  our  own,  having  also  its  own  planets 
and  its  own  moons.  These  stars,  or  suns,  are  so 
much  further  away  from  us  than  our  own  sun, 
that  but  a  speck  of  their  light  reaches  us,  and 
then  only  at  night,  when,  as  the  poets  would  say, 
our  sun  has  gone  to  its  resting  place. 

The  distances  between  bodies  in  the  solar  sys- 
tem is  so  immense  that,  like  the  number  of  dollars 
spent  in  the  Great  War,  the  number  of  miles  con- 
veys little,  or  no  impression.  But  picture  your- 
self in  an  express  train  going  at  the  average  rate 
of  30  miles  an  hour.  If  you  start  from  New  York 
and  travel  continuously  you  would  reach  San 
Francisco  in  4  days.  If  you  could  continue  your 
journey  around  the  earth  at  the  same  rate  you 
would  complete  it  in  35  days.  If  now  you  could 
travel  into  space  and  to  the  moon,  still  with  the 
same  velocity,  you  would  reach  it  in  350  days. 
Having  reached  the  moon,  you  could  circumscribe 
it  with  the  same  express  train  in  8  days,  as  com- 
pared to  the  35  days  it  would  take  you  to  circum- 
scribe the  earth.  If  instead  of  travelling  to  the 
moon  you  would  book  your  passage  for  the  sun 
you,  or  rather  your  descendants,  would  get  there 
in  350  years,  and  it  would  then  take  them  10 
additional  years  to  travel  around  the  sun. 


From  Newton  to  Einstein  45 

Immense  as  these  distances  are,  they  are  small 
as  compared  to  the  distances  that  separate  us 
from  the  stars.  It  takes  light  which,  instead  of 
travelling  30  miles  an  hour,  travels  186,000  miles 
a  second,  about  8  minutes  to  get  to  us  from  the 
sun,  and  a  little  over  4  years  to  reach  us  from  the 
nearest  star.  The  light  from  some  of  the  other 
stars  do  not  reach  us  for  several  hundred  years. 

The  Eclipse  of  the  Sun.  Now  to  return  to  an 
infinitesimal  part  of  the  universe — our  solar 
system.  We  have  seen  that  the  earth  travels 
around  the  sun,  and  the  moon  around  the  earth. 
At  some  time  in  the  course  of  these  revolutions 
the  moon  must  come  directly  between  the  earth 
and  the  sun.  Then  we  get  the  eclipse  of  the  sun. 
As  the  moon  is  smaller  than  the  earth,  only  a 
portion  of  the  earth's  surface  will  be  cut  off  from 
the  sun's  rays.  That  portion  which  is  so  cut  off 
suffers  a  total  eclipse.  This  explains  why  the 
eclipse  of  May,  1919,  which  was  a  total  one  for 
Brazil,  was  but  a  partial  one  for  us. 

Einstein9 s  Assertion  Re-stated.  Einstein  claimed 
that  a  ray  of  light  from  one  of  the  stars,  if  passing 
near  enough  to  the  surface  of  the  sun,  would  be 
appreciably  deflected  from  its  course;  and  he 
calculated  the  exact  amount  of  this  deflection. 
To  begin  with,  why  should  Einstein  suppose  that 


46  From  Newton  to  Einstein 

the  path  of  a  ray  of  light  would  be  affected  by  the 
sun? 

Newton's  law  of  gravitation  made  it  clear  that 
bodies  which  have  mass  attract  one  another.  If 
light  has  mass — and  very  recent  work  tends  to 
show  that  it  has — there  is  no  reason  why  light 
should  not  be  attracted  by  the  sun,  or  any  other 
planetary  body.  The  question  that  agitated 
scientists  was  not  so  much  whether  a  ray  of  light 
would  be  deviated  from  its  path,  but  to  what 
extent  this  deviation  would  take  place.  Would 
Einstein's  figures  be  confirmed? 

Of  the  bodies  within  our  solar  system  the  sun 
is  by  far  the  largest,  and  therefore  it  would  exert 
a  far  greater  pull  than  any  of  the  planets  on  light 
rays  coming  from  the  stars.  Under  ordinary 
conditions,  however*  the  sun  itself  shines  with  such 
brilliancy,  that  objects  around  it,  including  rays 
of  light  passing  near  its  surface,  are  wholly 
dimmed.  Hence  the  necessity  of  putting  our 
theory  to  the  test  only  when  the  moon  covers  up 
the  sun — when  there  is  a  total  eclipse  of  the  sun. 

A  Graphical  Representation.  Imagine  a  star  A> 
so  selected  that  as  its  light  comes  to  us  the  ray 
just  grazes  the  sun.  If  the  path  of  the  ray  is 
straight — if  the  sun  has  no  influence  on  it — then 
the  path  can  be  represented  by  the  line  AB.  If, 


From  Newton  to  Einstein 


47 


however,  the  sun  does  exert  a  gravitational  pull, 
then  its  real  path  will  be  AB',  and  to  an  observer 
on  the  earth  the  star  will  have  appeared  to  shift 
from  A  to  A'. 


What  the  Eclipse  Expedition  Set  Out  to  Do. 
Photographs  of  stars  around  the  sun  were  to  be 
taken  during  the  eclipse,  and  these  photographs 
compared  with  others  of  the  same  region  taken  at 
night,  with  the  sun  absent.  Any  apparent  shift- 
ing of  the  stars  could  be  determined  by  measuring 
the  distances  between  the  stars  as  shown  on  the 
photographic  plates. 

Three  Possibilities  Anticipated.  According  to 
Newton's  assumption,  light  consists  of  corpuscles, 
or  minute  particles,  emitted  from  the  source  of 
light.  If  this  be  true  these  particles,  having 
mass,  should  be  affected  by  the  gravitational  pull 
of  the  sun.  If  we  apply  Newton's  theory  of 
gravitation  and  make  use  of  his  formula,  it  can 
be  shown  that  such  a  gravitational  pull  would  dis- 


48  From* Newton  to  'Einstein 

place  the  ray  of  light  by  an  average  amount  equal 
to  0.75  (seconds  of  angular  distance.)*  .On  the 
other  hand,  where  lig^t  is  regarded  as  waves  set 
in  motion  in  the  "ether"  of  space  (the  wave 
theory  of  light),  and  wjiere  weight  is  denied  light 
altogether,  no  deviation  need  be  expected.  Finaljfo 
there  is  a  third  alternative:  Einstein's.  \Liglft, 
says  Einstein,  has  mass,  and  therefore  pro^ajaljr 
weight.  Mass  is  the  matter  light  contains; 
weight  represents  pull  by  gravity.  Light  rays 
will  be  attracted  by  the  sun,  but  according  to 
Einstein's  theory  of  gravitation  the  sun's  gravi- 
tational pull  will  displace  the  rays  by  an  average 
amount  equal  to  1.75  (seconds  of  angular  dis- 
tance). 

The  Expeditions.  That  science  is  highly  inter- 
national, despite  many  recent  examples  to  the 
contrary,  is  evidenced  by  this  British  Eclipse 
Expedition.  Here  was  a  theory  propounded  by 
one  who  had  accepted  a  chair  of  physics  in  the 
university  of  Berlin,  and  across  the  English  Chan- 
nel were  Germany's  mortal  enemies  making  elab- 
orate preparations  to  test  the  validity  of  the 
Berlin  professor's  theory. 

*  A  circle — in  our  case  the  horizon — is  measured  by  divid- 
ing the  circumference  into  360  parts;  each  part  is  called  a 
degree.  Each  degree  is  divided  into  60  minutes,  and  each 
minute  into  60  seconds. 


From  Newton  to  Einstein  49 

The  British  Astronomical  Society  began  to  plan 
the  eclipse  expedition  even  before  the  outbreak 
of  the  Great  War.  During  the  years  that  fol- 
lowed, despite  the  destinies  of  nations  which  hung 
on  threads  from  day  to  day,  despite  the  darkest 
hours  in  the  history  of  the  British  people,  our 
English  astronomers  continued  to  give  attention 
to  the  details  of  the  proposed  expedition.  When 
the  day  of  the  eclipse  came  all  was  in  readiness. 

One  expedition  under  Dr.  Crommelin  was  sent 
to  Sobral,  Brazil;  another,  under  Prof.  Edding- 
ton,  to  Principe,  an  island  off  the  west  coast  of 
Africa.  In  both  these  places  a  total  eclipse  was 
anticipated. 

The  eclipse  occurred  on  May  29,  1919.  It 
lasted  for  six  to  eight  minutes.  Some  15  photo- 
graphs, with  an  average  exposure  of  five  to  six 
seconds,  were  taken.  Two  months  later  another 
series  of  photographs  of  the  same  region  were 
taken,  but  this  time  the  sun  was  no  longer  in  the 
midst  of  these  stars. 

The  photographs  were  brought  to  the  famous 
Greenwich  Observatory,  near  London,  and  the 
astronomers  and  mathematicians  began  their 
laborious  measurements  and  calculations. 

On  November  6,  at  the  meeting  of  the  Royal 
Society,  the  result  was  announced.  The  Sobral 


50  From  Newton  to  Einstein 

expedition  reported  1.98;  the  Principe  expedition 
1.62.  The  aver  age  was  1.8.  Einstein  had  predicted 
1.75,  Newton  might  have  predicted  0.75,  and 
the  orthodox  scientists  would  have  predicted  0. 
There  could  now  no  longer  be  any  question  as  to 
which  of  the  three  theories  rested  on  a  sure  foun- 
dation. To  quote  Sir  Frank  Dyson,  the  Astron- 
omer Royal:  "After  a  careful  study  of  the  plates 
I  am  prepared  to  say  that  there  can  be  no  doubt 
that  they  confirm  Einstein's  prediction.  A  very 
definite  result  has  been  obtained  that  light  is 
deflected  in  accordance  with  Einstein's  law  of 
gravitation."  * 

Where  Did  Einstein  Get  His  Idea  of  Gravitation? 
In  1905  Einstein  published  the  first  of  a  series  of 
papers  supporting  and  extending  a  theory  of  time 
and  space  to  which  the  name  "the  theory  of 
relativity"  had  been  given.  These  views  as 
expounded  by  Einstein  came  into  direct  conflict 
with  Newton's  ideas  of  time  and  space,  and  also 
with  Newton's  law  of  gravitation.  Since  Ein- 
stein Had  more  faith  in  his  theory  of  relativity 
than  in  Newton's  theory  of  gravitation,  Einstein 
so  changed  the  latter  as  to  make  it  harmonize  with 
the  former.  More  will  be  said  on  this  subject. 

*  See  page  113. 


From  Newton  to  Einstein  51 

Let  not  the  reader  misunderstand.  Newton 
was  not  wholly  in  the  wrong;  he  was  only  ap- 
proximately right.  With  the  knowledge  existing 
in  Newton's  day  Newton  could  have  done  no 
more  than  he  did;  no  mortal  could  have  done 
more.  But  since  Newton's  day  physics — and 
science  in  general — has  advanced  in  great  strides, 
and  Einstein  can  interpret  present-day  knowledge 
in  the  same  masterful  fashion  that  Newton  could 
in  his  day.  With  more  facts  to  build  upon,  Ein- 
stein's law  of  gravitation  is  more  universal  than 
Newton's;  it  really  includes  Newton's. 

But  now  we  must  turn  our  attention  very  briefly 
to  the  theory  of  relativity — the  theory  that  led 
up  to  Einstein's  law  of  gravitation. 

The  Theory  of  Relativity.  The  story  goes  that 
Einstein  was  led  to  his  ideas  by  watching  a  man 
fall  from  a  roof.  This  story  bears  a  striking 
similarity  to  Newton  and  the  apple.  Perhaps 
one  is  as  true  as  the  other.* 

However  that  may  be,  the  principle  of  rela- 
tivity is  as  old  as  philosophical  thought,  for  it 
denies  the  possibility  of  measuring  absolute  time, 
or  absolute  space.  All  things  are  relative.  We 
say  that  it  takes  a  "long  time"  to  get  from  New 
York  to  Albany;  long  as  compared  to  what? 

*  See  Note  4. 


52  From  Newton  to  Einstein 

long,  perhaps,  as  compared  to  the  time  it  takes  to 
go  from  New  York  City  to  Brooklyn.  We  say 
the  White  House  is  "large";  large  when  compared 
to  a  room  in  an  apartment.  But  we  can  just  as 
well  reverse  our  ideas  of  time  and  distance.  The 
time  it  takes  to  go  from  New  York  to  Albany  is 
"short"  when  compared  to  the  time  it  takes  to 
go  from  New  York  to  San  Francisco.  The  size  of 
the  White  House  is  "small"  when  compared  to 
the  size  of  the  city  of  Washington. 

Let  us  take  another  illustration.  Every  time 
the  earth  turns  on  its  axis  we  mark  down  as  a  day. 
With  this  as  a  basis,  we  say  that  it  takes  a  little 
over  365  days  for  the  earth  to  complete  its  revo- 
lution around  the  sun,  and  our  365  days  we  call  a 
year.  But  now  consider  some  of  our  other 
planets.  With  our  time  as  a  basis,  it  takes  Jupi- 
ter or  Saturn  10  hours  to  turn  on  its  axis,  as  com- 
pared to  the  24  hours  it  takes  the  earth  to  turn. 
Saturn's  day  is  less  than  one-half  our  day,  and 
our  day  is  more  than  twice  Saturn's — that  is, 
according  to  the  calculations  of  the  inhabitants 
of  the  earth.  Mercury  completes  her  circuit 
around  the  sun  in  88  days;  Neptune,  in  164 
years.  Mercury's  year  is  but  one-fourth  ours, 
Neptune's,  164  times  ours.  And  observers  at 
Mercury  and  Neptune  would  regard  us  from 


From  Newton  to  Einstein  53 

their  standard  of  time,  which  differs  from  our 
standard. 

You  may  say,  why  not  take  our  standard  of 
time  as  the  standard,  and  measure  everything  by 
it?  But  why  should  you?  Such  a  selection 
would  be  quite  arbitrary.  It  would  not  be 
based  on  anything  absolute,  but  would  merely 
depend  on  our  velocity  around  the  sun. 

These  ideas  are  old  enough  in  metaphysics. 
Einstein's  improvement  of  them  consists  not 
merely  in  speculating  about  them,  but  in  giving 
them  mathematical  form. 

The  Origin  of  the  Theory  of  Relativity.  A  train 
moves  with  reference  to  the  earth.  The  earth 
moves  with  reference  to  the  sun.  We  say  the 
sun  is  stationary  and  the  earth  moves  around 
the  sun.  But  how  do  we  know  that  the  sun  itself 
does  not  move  with  reference  to  some  other  body? 
How  do  we  know  that  our  planetary  system,  and 
the  stars,  and  the  cosmos  as  a  whole  is  not  in 
motion? 

There  is  no  way  of  answering  such  a  question 
unless  we  could  get  a  point  of  reference  which  is 
fixed — fixed  absolutely  in  space. 

We  have  already  alluded  to  our  view  of  the 
nature  of  light,  known  as  the  wave  theory  of 
light.  This  theory  postulates  the  existence  of 


54  From  Newton  to  Einstein 

an  all-pervading  "ether"  in  space.  Light  sets  up 
wave  disturbances  in  this  ether,  and  is  thus 
propagated.  If  the  ocean  were  the  ether,  the 
waves  of  the  ocean  would  compare  with  the  waves 
set  up  by  the  ether. 

But  what  is  this  ether?  It  cannot  be  seen.  It 
defies  weight.  It  permeates  all  space.  It  per- 
meates all  matter.  So  say  the  exponents  of 
this  ether.  To  the  layman  this  sounds  very 
much  like  another  name  for  the  Deity.  To  Sir 
Oliver  Lodge  it  represents  the  spirits  of  the  de- 
parted. 

To  us,  of  importance  is  the  conception  that  this 
ether  is  absolutely  stationary.  Such  a  concep- 
tion is  logical  if  the  various  developments  in 
optics  and  electricity  are  considered.  But  if 
absolutely  stationary,  then  the  ether  is  the  long- 
sought-for  point  of  reference,  the  guide  to  deter- 
mine the  motion  of  all  bodies  in  the  universe. 

The  Famous  Experiment  Performed  by  Prof. 
Michelson.  If  there  is  an  ether,  and  a  stationary 
ether,  and  if  the  earth  moves  with  reference  to 
this  ether,  the  earth,  in  moving,  must  set  up 
ether  "currents" — just  as  when  a  train  moves  it 
sets  up  air  currents.  So  reasoned  Michelson,  a 
young  Annapolis  graduate  at  the  time.  And 
forthwith  he  devised  a  crucial  experiment  the 


From  Newton  to  Einstein  55 

explanation  of  which  we  can  simplify  by  the  fol- 
lowing analogy: 

Which  is  the  quicker,  to  swim  up  stream  a  cer- 
tain length,  say  a  hundred  yards,  and  back  again, 
or  across  stream  the  same  length  and  back  again? 
The  swimmer  will  answer  that  the  up-and-down 
journey  is  longer.* 

Our  river  is  the  ether.  The  earth,  if  moving  in 
this  ether,  will  set  up  an  ether  stream,  the  up 
stream  being  parallel  to  the  earth's  motion.  Now 
suppose  we  send  a  beam  of  light  a  certain  distance 
up  this  ether  stream  and  back,  and  note  the  time; 
and  then  turn  the  beam  of  light  at  right  angles 
and  send  it  an  equal  distance  across  the  stream 
and  back,  and  note  the  time.  How  will  the  time 
taken  for  light  to  travel  in  these  two  directions 
compare?  Reasoning  by  analogy,  the  up-and- 
down  stream  should  take  longer. 

Michelson's  results  did  not  accord  with  analogy. 
No  difference  in  time  could  be  detected  between 
the  beam  of  light  travelling  up-and-down,  and 
across-and-back. 

But  this  was  contrary  to  all  reason  if  the  pos- 
tulate of  an  ether  was  sound.  Must  we  then 
revise  our  ideas  of  an  ether?  Perhaps  after  all 
there  is  no  ether. 

*  See  Note  5. 


56  From  Newton  to  Einstein 

But  if  no  ether,  how  are  we  to  explain  the 
propagation  of  light  in  space,  and  various  elec- 
trical phenomena  connected  with  it,  such  as  the 
Hertzian,  or  wireless  waves? 

There  was  another  alternative,  one  suggested 
by  Larmor  in  England  and  Lorentz  in  Holland, — 
that  matter  is  contracted  in  the  direction  of  its 
motion  through  the  ether  current.  To  say  that 
bodies  are  actually  shortened  in  the  direction  of 
their  motion — by  an  amount  which  increases  as 
the  velocity  of  these  bodies  approaches  that  of 
light — is  so  revolutionary  an  idea  that  Larmor 
and  Lorentz  would  hardly  have  adopted  such  a 
viewpoint  but  for  the  fact  that  recent  investiga- 
tions into  the  nature  of  matter  gave  basis  for  such 
belief. 

Matter,  it  has  been  shown,  is  electrical  in  na- 
ture. The  forces  which  hold  the  particles  to- 
gether are  electrical.  Lorentz  showed  that  math- 
ematical formulas  for  electrical  forces  could  be 
developed  which  would  inevitably  lead  to  the 
view  that  material  bodies  contract  in  the  direc- 
tion of  their  motion.* 

"But  this  is  ridiculous,"  you  say;  "if  I  am 
shorter  in  one  direction  than  in  another  I  would 
notice  it."  You  would  if  some  things  were 
shortened  and  others  were  not.  But  if  all  things 

*  See  Note  6. 


From  Newton  to  Einstein  57 

pointing  in  a  certain  direction  are  shortened  to 
an  equal  extent,  how  are  you  going  to  notice  it? 
Will  you  apply  the  yard  stick?  That  has  been 
shortened.  Will  you  pass  judgment  with  the 
help  of  your  eyes?  But  your  retina  has  also 
contracted.  In  brief,  if  all  things  contract  to 
the  same  amount  it  is  as  if  there  were  no  con- 
traction at  all. 

Lorentz's  Plausible  Explanation  Really  Deepens 
the  Mystery.  The  startling  ideas  just  outlined 
have  opened  up  several  new  vistas,  but  they  have 
left  unanswered  the  two  problems  we  set  out  to 
solve:  whether  there  is  an  ether,  and  if  so, 
what  is  the  velocity  of  the  earth  in  reference  to 
this  ether?  Lorentz  maintains  that  there  is  an 
ether,  but  the  velocities  of  bodies  relative  to  it 
must  forever  remain  a  mystery.  As  you  change 
your  position  your  distances  change;  you  change; 
everything  about  you  changes  accordingly;  and 
all  basis  for  comparison  is  lost.  Nature  has 
entered  into  a  conspiracy  to  keep  you  ignorant. 

Einstein  Comes  upon  the  Scene.  Einstein 
starts  with  the  assumption  that  there  is  no  pos- 
sible way  of  identifying  this  ether.  Suppose  we 
ignore  the  ether  altogether,  what  then?* 

If  we  do  ignore  the  ether  we  no  longer  have 

*  See  Note  7. 


58  From  Newton  to  Einstein 

any  absolute  point  of  reference;  for  if  the  ether 
is  considered  stationary  the  velocity  of  all  bodies 
within  the  ether  may  be  referred  to  it;  any  point 
in  space  may  be  considered  a  fixed  point.  If, 
however,  there  is  no  ether,  or  if  we  are  to  ignore 
it,  how  are  we  to  get  the  velocity  of  bodies  in 
space? 

The  Principle  of  Relativity.  If  we  are  to 
believe  in  the  "causal  relationship  between  only 
such  things  as  lie  within  the  realm  of  observation," 
then  observation  teaches  us  that  bodies  move  only 
relative  to  one  another,  and  that  the  idea  of 
absolute  motion  of  a  body  in  space  is  meaning- 
less. Einstein,  therefore,  postulates  that  there 
is  no  such  thing  as  absolute  motion,  and  that  all 
we  can  discuss  is  the  relative  motion  of  one 
body  with  respect  to  another.  This  is  just  as 
logical  a  deduction  from  Michelson's  experiment 
as  the  attempt  to  explain  Michelson's  anomalous 
results  in  the  light  of  an  all-pervading  ether. 

Consider  for  a  moment  Newton's  scheme.  This 
great  pioneer  pictured  an  absolute  standard  of 
position  in  space  relative  to  which  all  velocities 
are  measured.  Velocities  were  measured  by 
noting  the  distance  covered  and  dividing  the  result 
by  the  time  taken  to  cover  the  distance.  Space 
was  a  definite  entity;  and  so  was  time.  "Time," 


From  Newton  to  Einstein  59 

said  Newton,  "flows  evenly  on,"  independent  of 
aught  else.  To  Newton  time  and  space  were 
entirely  different,  in  no  way  to  be  confounded. 

Just  as  Newton  conceived  of  absolute  space,  so 
he  conceived  of  absolute  time.  From  the  latter 
standard  of  reference  the  idea  of  a  "simultaneity 
of  events"  at  different  places  arose.  But  now  if 
there  is  no  standard  of  reference,  if  the  ether  does 
not  exist  or  does  not  function,  if  two  points  A  and 
B  cannot  be  referred  to  a  third,  and  fixed  point  C, 
how  can  we  talk  of  "simultaneity  of  events"  at 
A  and  B? * 

In  fact,  Einstein  shows  that  if  all  you  can  speak 
about  is  relative  motion,  then  one  event  which 

H 


B  <iA 

takes  say  one  minute  on  one  planet  would  not 
take  one  minute  on  another.  For  consider  two 
bodies  in  space,  say  the  planets  Venus  and  the 
earth,  with  an  observer  B  on  Venus  and  another 
A  on  the  earth.  B  notes  the  time  taken  for  a 
ray  of  light  to  travel  from  B  to  the  distance  M . 
*  See  Note  8. 


60  From  Newton  to  Einstein 

on  the  earth  has  means  of  observing  the  same 
event.  B  records  one  minute.  A  is  puzzled, 
for  his  watch  records  a  little  more  than  one 
minute.  What  is  the  explanation?  Granting 
that  the  two  clocks  register  the  same  time  to 
start  with,  and  assuming  further  Einstein's  hy-^ 
pothesis  that  the  velocity  of  light  is  independent  of 
its  source,  the  difference  in  time  is  due  to  the  fact 
that  the  planet  Venus  moves  with  reference  to 
the  observer  on  the  earth;  so  that  A  in  reality 
does  not  measure  the  path  BM  and  M B,  but 
BM'  and  M'B',  where  BB'  represents  the  dis- 
tance Venus  itself  has  moved  in  the  interval. 
And  if  you  put  yourself  in  J5's  position  on  Venus 
the  situation  is  exactly  reversed.  All  of  which  is 
simply  another  way  of  saying  that  what  is  a  cer- 
tain time  on  one  body  in  space  is  another  time  on 
another  body  in  space.  There  is  nothing  definite 
in  time. 

Prof.  Cohen's  Illustration.  Further  bewildering 
possibilities  are  clearly  outlined  in  this  apt  illus- 
tration: "If  when  you  are  going  away  on  a  long 
and  continuous  journey  you  write  home  at  regular 
intervals,  you  should  not  be  surprised  that  with 
the  best  possible  mail  service  your  letters  will 
reach  home  at  progressively  longer  intervals, 
since  each  letter  will  have  a  greater  distance  to 


From  Newton  to  Einstein  61 

travel  than  its  predecessor.  If  you  were  armed 
with  instruments  to  hear  the  home  clock  ticking, 
you  would  find  that  as  your  distance  from  home 
keeps  on  increasing,  the  intervals  between  the  suc- 
cessive ticks  (that  is,  its  seconds)  grow  longer,  so 
that  if  you  travelled  with  the  velocity  of  sound 
the  home  clock  would  seem  to  slow  down  to  a 
standstill — you  would  never  hear  the  next  tick. 

"Precisely  the  same  is  true  if  you  substitute 
light  rays  for  sound  waves.  If  with  the  naked 
eye  or  with  a  telescope  you  watch  a  clock  moving 
away  from  you,  you  will  find  that  its  minute  hand 
takes  a  longer  time  to  cover  its  five-minute  inter- 
vals than  does  the  chronometer  in  your  hand,  and 
if  the  clock  travelled  with  the  velocity  of  light 
you  would  forever  see  the  minute  hand  at  pre- 
cisely the  same  point.  That  which  is  true  of  the 
clock  is,  of  course,  also  true  of  all  time  intervals 
which  it  measures,  so  that  if  you  moved  away 
from  the  earth  with  the  velocity  of  light  every- 
thing on  it  would  appear  as  still  as  on  a  painted 
canvas." 

Your  time  has  apparently  come  to  a  standstill 
in  one  position  and  is  moving  in  another!  All 
this  seems  absurd  enough,  but  it  does  show  that 
time  alone  has  little  meaning. 

Minkowski's  Conclusion.    The  relativity  the- 


From  Newton  to  Einstein 


ory  requires  that  we  thoroughly  reorganise  our 
method  of  measuring  time.  But  this  is  inti- 
mately associated  with  our  method  of  measuring 
space,  the  distance  between  two  points.  As  we 
proceed  we  find  that  space  without  time  has  little 
meaning,  and  vice  versa.  This  leads  Minkowski 
to  the  conclusion  that  "time  by  itself  and  space 
by  itself  are  mere  shadows;  they  are  only  two 
aspects  of  a  single  and  indivisible  manner  of  co- 
ordinating the  facts  of  the  physical  world."  Ein- 
stein incorporated  this  time-space  idea  in  his 
theory  of  relativity. 

How  We  Measure  a  Point  in  Space.  Suppose 
I  say  to  you  that  the  chemical  laboratory  of 
Columbia  University  faces  Broadway;  would 
that  locate  the  laboratory?  Hardly,  for  any 
building  along  Broadway  would  face  Broadway. 
But  suppose  I  add  that  it  is  situated  at  Broadway 
and  117th  Street,  south-east?  there  could  be  little 
doubt  then.  But  if,  further,  this  laboratory 
would  occupy  but  part  of  the  building,  say  the 
third  floor;  then  the  situation  would  be  specified 
by  naming  Broadway,  117th  Street  S.  E.,  third 
floor.  If  Broadway  represents  length,  117th 
Street  width,  and  third  floor  height,  we  can  see 
what  is  meant  when  we  say  that  three  dimensions 
are  required  to  locate  a  position  in  space. 


From  Newton  to  Einstein  63 

The  Fourth  Dimension.  A  point  on  a  line  may 
be  located  by  one  dimension;  a  point  on  a  wall 
requires  two  dimensions;  a  point  in  the  room,  like 
the  chemical  laboratory  above  ground,  needs 
three.  The  layman  cannot  grasp  the  meaning 
of  a  fourth  dimension;  yet  the  mathematician 
does  imagine  it,  and  plays  with  it  in  mathemat- 
ical terms.  Minkowski  and  Einstein  picture 
time  as  the  fourth  dimension.  To  them  time 
occupies  no  more  important  position  than  length, 
breadth,  or  thickness,  and  is  as  intimately  related 
to  these  three  as  the  three  are  to  one  another. 
H.  G.  Wells,  the  novelist,  has  beautifully  caught 
this  spirit  when  in  his  novel,  "The  Time  Ma- 
chine," he  makes  his  hero  travel  backwards  and 
forwards  along  time  just  as  a  man  might  go  north 
or  south.  When  the  man  with  his  time  machine 
goes  forward  he  is  in  the  future;  when  he  goes 
backwards  he  is  in  the  past. 

In  reality,  if  we  stop  to  think  a  minute,  there 
is  no  valid  reason  for  the  non-existence  of  a  fourth 
dimension.  If  one,  two  and  three  dimensions, 
why  not  four — and  five  and  six,  for  that  matter? 
Theoretically  at  least  there  is  no  reason  why  the 
limit  should  be  set  at  three.  However,  our  minds 
become  sluggish  when  we  attempt  to  picture 
dimensions  beyond  three;  just  as  an  extraordi- 


64  From  Newton  to  Einstein 

nary  effort  on  our  part  is  needed  to  follow  Einstein 
when  he  "juggles"  with  space  and  time. 

Our  difficulty  in  imagining  four  dimensions  may 
be  likened  to  the  difficulty  two-dimensioned 
beings  would  experience  in  imagining  us,  beings  of 
the  conventional  three  dimensions.  Suppose 
these  two-dimensional  beings  were  living  on  the 
surface  of  the  earth;  what  could  they  see? 
They  could  see  nothing  below  and  nothing  above 
the  surface.  They  would  see  shifting  surfaces 
as  we  walked  about,  but  being  sensitive  to  length 
and  breadth  only,  and  not  to  height,  they  could 
gain  no  notion  whatsoever  of  what  we  really 
look  like.  It  is  thus  with  us  when  we  attempt 
to  picture  four-dimensional  space. 

Perhaps  the  analogy  of  the  motion  picture  may 
help  us  somewhat.  As  everybody  knows,  these 
motion  pictures  consist  of  a  series  of  photographs 
which  are  shown  in  rapid  succession  on  the  screen. 
Each  photograph  by  itself  conveys  a  sensation  of 
space,  that  is,  of  three  dimensions;  but  one  pho- 
tograph rapidly  following  another  conveys  the 
sensation  of  space  and  time — four  dimensions. 
Space  and  time  are  interlinked. 

The  Time-space  Idea  Further  Developed.  We 
tave  already  alluded  to  the  fact  that  objects  in 
space  moving  with  different  velocities  build  up 


^msc 


From  Newton  to  Einstein  65 

different  time  intervals.  Thus  the  velocity  of  the 
star  Arcturus,  if  compared  with  reference  to  the 
earth,  moves  at  the  rate  of  200  miles  a  second. 
Its  motion  through  space  is  different  from  ours. 
Objects  which,  according  to  Lorentz,  contract 
in  the  direction  of  their  motion  to  an  extent 
proportional  to  their  velocity,  will  contract  dif- 
ferently on  the  surface  of  Arcturus  than  on  the 
earth.  Our  space  is  not  Arcturus'  space;  neither 
is  Arcturus'  time  our  time.  And  what  is  true 
of  the  discrepancies  existing  between  the  space 
and  time  conceptions  of  the  earth  and  Arcturus  is 
true  of  any  other  two  bodies  in  space  moving  at 
different  velocities. 

But  is  there  no  relationship  existing  between 
the  space  and  time  of  one  body  in  the  universe  as 
compared  to  the  space  and  time  of  another?  Can 
we  not  find  something  which  holds  good  for  all 
bodies  in  the  universe?  We  can.  We  can  express 
it  mathematically.  It  is  the  concept  of  time  and 
space  interlinked;  of  time  as  the  fourth  dimen- 
sion, length,  breadth  and  thickness  being  the 
other  three;  of  time  as  one  of  four  co-ordinates 
and  at  right  angles  to  the  other  three  (a  situation 
which  requires  a  terrific  stretch  of  the  imagina- 
tion to  visualize) .  The  four  dimensions  are  suffi- 
cient to  co-ordinate  the  time-space  relationships 


66  From  Newton  to  Einstein 

of  all  bodies  in  the  cosmos,  and  hence  have  a 
universality  which  is  totally  lacking  when  time 
and  space  are  used  independently  of  one  another. 
The  four  components  of  our  time-space  are  up- 
and-down,  right-and-left,  backwards-and-for- 
wards,  and  sooner-and-later. 

"Strain"  and  "Distortion"  in  Space.  The 
four-dimensional  unit  has  been  given  the  name 
"world-line,"  for  the  "world-line"  of  any  particle 
in  space  is  in  reality  a  complete  history  of  that 
particle  as  it  moves  about  in  space.  Particles, 
we  know,  attract  one  another.  If  each  particle  is 
represented  by  a  world-line  these  world-lines  will 
be  deflected  from  their  course  owing  to  such 
attraction. 

Imagine  a  bladder  representing  the  universe, 
with  lines  on  it  representing  world-lines.  Now 
squeeze  the  bladder.  The  world-lines  are  bent 
in  various  directions;  they  are  "distorted." 
This  illustrates  the  influence  of  gravity  on  these 
world-lines;  it  is  the  "strain"  brought  about  due 
to  the  force  of  attraction.  The  distorted  bladder 
illustrates  even  more,  for  it  is  a  true  representa- 
tion of  the  real  world. 

How  Einstein's  Conception  of  Time  and  Space 
Led  to  a  New  View  of  Gravitation.  In  our  con- 
ventional language  we  speak  of  the  sun  as  exerting 


From  Newton  to  Einstein  67 

a  "force"  on  the  earth.  We  have  seen,  however, 
that  this  force  brings  about  a  "distortion"  or 
"strain"  in  world-lines;  or,  what  amounts  to  the 
same  thing,  a  "distortion"  or  "strain"  of  time 
and  space.  The  sun's  "force,"  the  "force"  of 
any  body  in  space,  is  the  "force"  due  to  gravity; 
and  these  "forces"  may  now  be  treated  in  terms 
of  the  laws  of  time  and  space.  "The  earth," 
Prof.  Eddington  tells  us,  "moves  in  a  curved 
orbit,  not  because  the  sun  exerts  any  direct  pull, 
but  because  the  earth  is  trying  to  find  the  short- 
est way  through  a  space  and  time  which  have 
been  tangled  up  by  an  influence  radiating  from 
the  sun."  * 

At  this  point  Newton's  conceptions  fail,  for 
his  views  and  his  laws  do  not  include  "strains" 
in  space.  Newton's  law  of  gravitation  must  be 
supplanted  by  one  which  does  include  such  dis- 
tortions. It  is  Einstein's  great  glory  to  have  sup- 
plied us  with  this  new  law. 

Einstein's  Law  of  Gravitation.  This  appears  to 
be  the  only  law  which  meets  all  requirements. 
It  includes  Newton's  law,  and  cannot  be  distin- 
guished from  it  if  our  experiments  are  confined 
to  the  earth  and  deal  with  relatively  small 
velocities.  But  when  we  betake  ourselves  to 

*  See  Note  9. 


68  From  Newton  to  Einstein 

some  orbits  in  space,  with  a  gravitational  pull 
much  greater  than  the  earth's,  and  when  we  deal 
with  velocities  comparable  to  that  of  light,  the 
differences  become  marked. 

Einstein9 s  Theory  Scores  Its  First  Great  Victory. 
In  the  beginning  of  this  chapter  we  referred  to 
the  elaborate  eclipse  expedition  sent  by  the  Brit- 
ish to  test  the  validity  of  Einstein's  new  theory 
of  gravitation.  The  British  scientists  would 
hardly  have  expended  so  much  time  and  energy 
on  this  theory  of  Einstein's  but  for  the  fact  that 
Einstein  had  already  scored  one  great  victory. 
What  was  it? 

Imagine  but  a  single  planet  revolving  about  the 
sun.  According  to  Newton's  law  of  gravitation, 
the  planet's  path  would  be  that  of  an  ellipse — 
that  is,  oval — and  the  planet  would  travel  indef- 
initely along  this  path.  According  to  Einstein 
the  path  would  also  be  elliptical,  but  before  a 
revolution  would  be  quite  completed,  the  planet 
would  start  along  a  slightly  advanced  line,  form- 
ing a  new  ellipse  slightly  in  advance  of  the  first. 
The  elliptic  orbit  slowly  turns  in  the  direction  in 
which  the  planet  is  moving.  After  many  years — 
centuries — the  orbit  will  be  in  a  different  direction. 

The  rapidity  of  the  orbit's  change  of  direction 
depends  on  the  velocity  of  the  planet^  Mercury 


From  Newton  to  Einstein 


moving  at  the  rate  of  30  miles  a  secon$  is  the  fast- 
est among  the  planets.  It  has  the  further  ad- 
vantage over  Venus  or  the  earth  in  that  its  orbit, 
as  we  have  said,  is  an  ellipse,  whereas  the  orbits 
of  Venus  and  the  earth  are  nearly  circular;  and 
how  are  you  going  to  tell  in  which  direction  a 
circle  is  pointing? 

Observation  tells  us  that  the  orbit  of  Mercury 
is  advancing  at  the  rate  of  574  seconds  (of  arc) 
per  century.  We  can  calculate  how  much  of  this 
is  due  to  the  gravitational  influence  of  other 
planets.  It  amounts  to  532  seconds  per  century. 
What  of  the  remaining  42  seconds? 

You  might  be  inclined  to  attribute  this  short- 
coming to  experimental  error.  But  when  all 
such  possibilities  are  allowed  for  our  mathe- 
maticians assure  us  that  the  discrepancy  is  30 
times  greater  than  any  possible  experimental 
error. 

This  discrepancy  between  theory  and  observa- 
tion remained  one  of  the  great  puzzles  in  astron- 
omy until  Einstein  cleared  up  the  mystery. 
According  to  Einstein's  theory  the  mathematics  of 
the  situation  is  simply  this:  in  one  revolution  of 
the  planet  the  orbit  will  advance  by  a  fraction  of  a 
revolution  equal  to  three  times  the  square  of  the 
ratio  of  the  velocity  of  the  planet  to  the  velocity 


70  From  Newton  to  Einstein 

of  light.  When  we  allow  mathematicians  to 
work  this  out  we  get  the  figure  43,  which  is 
certainly  close  enough  to  42  to  be  called  identical 
with  it. 

Stitt  Another  Victory?  Einstein's  third  pre- 
diction— the  shifting  of  spectral  lines  toward  the 
red  end  of  the  spectrum  in  the  case  of  light  coming 
to  us  from  the  stars  of  appreciable  mass — seems 
to  have  been  confirmed  recently  (March,  1920). 
"The  young  physicists  in  Bonn,"  writes  Prof. 
Einstein  to  a  friend,  "have  now  as  good  as 
certainty  (so  gut  wie  sicker)  proved  the  red 
displacement  of  the  spectral  lines  and  have 
cleared  up  the  grounds  of  a  previous  disappoint- 
ment." 

Summary.  Velocity,  or  movement  in  space,  is 
at  the  basis  of  Einstein's  work,  as  it  was  at  the 
basis  of  Newton's.  But  time  and  space  no  longer 
have  the  distinct  meanings  that  they  had  when 
examined  with  the  help  of  Newton's  equations. 
Time  and  space  are  not  independent  but  inter- 
dependent. They  are  meaningless  when  treated 
as  separate  entities,  giving  results  which  may 
hold  for  one  body  in  the  universe  but  do  not  hold 
for  any  other  body.  To  get  general  laws  which 
are  applicable  to  the  cosmos  as  a  whole  the  Fun- 
damentals of  Mechanics  must  be  united. 


From  Newton  to  Einstein  71 

Einstein's  great  achievement  consists  in  apply- 
ing this  revised  conception  of  space  and  time  to 
elucidate  cosmical  problems.  "World-lines," 
representing  the  progress  of  particles  in  space, 
consisting  of  space-time  combinations  (the  four 
dimensions),  are  "strained"  or  "distorted"  in 
space  due  to  the  attraction  that  bodies  exhibit 
for  one  another  (the  force  of  gravitation).  On 
the  other  hand,  gravitation  itself — more  universal 
than  anything  else  in  the  universe — may  be  inter- 
preted in  terms  of  strains  on  world-lines,  or,  what 
amounts  to  the  same  thing,  strains  of  space-time 
combinations.  This  brings  gravitation  within 
the  field  of  Einstein's  conception  of  time  and 
space. 

That  Einstein's  conception  of  the  universe  is  an 
improvement  upon  that  of  Newton's  is  evidenced 
by  the  fact  that  Einstein's  law  explains  all  that 
Newton's  law  does,  and  also  other  facts  which 
Newton's  law  is  incapable  of  explaining.  Among 
these  may  be  mentioned  the  distortion  of  the  oval 
orbits  of  planets  round  the  sun  (confirmed  in  the 
case  of  the  planet  Mercury),  and  the  deviation  of 
light  rays  in  a  gravitational  field  (confirmed  by 
the  English  Solar  Eclipse  Expedition). 

Einstein's  Theories  and  the  Inferences  to  be 
Drawn  from  Them.  Einstein's  theories,  sup- 


72  From  Newton  to  Einstein 


ported  as  they  are  by  very  convincing  experi- 
ments, will  probably  profoundly  influence  philo- 
sophic and  perhaps  religious  thought,  but  they 
can  hardly  be  said  to  be  of  immediate  consequence 
to  the  man  in  the  street.  As  I  have  said  else- 
where, Einstein's  theories  are  not  going  to  add 
one  bushel  of  wheat  to  war-torn  and  devastated 
Europe,  but  in  their  conception  of  a  cosmos 
decidedly  at  variance  with  anything  yet  con- 
ceived by  any  school  of  philosophy,  they  will 
attract  the  universal  attention  of  thinking  men 
in  all  countries.  The  scientist  is  immediately 
struck  by  the  way  Einstein  has  utilized  the 
various  achievements  in  physics  and  mathe- 
matics to  build  up  a  co-ordinated  system  showing 
connecting  links  where  heretofore  none  were  per- 
ceived. The  philosopher  is  equally  fascinated 
with  a  theory,  which,  in  detail  extremely  com- 
plex, shows  a  singular  beauty  of  unity  in  design 
when  viewed  as  a  whole.  The  revolutionary 
ideas  propounded  regarding  time  and  space,  the 
brilliant  way  in  which  the  most  universal  property 
of  matter,  gravitation,  is  for  the  first  time  linked 
up  with  other  properties  of  matter,  and,  above  all, 
the  experimental  confirmation  of  several  of  his 
more  startling  predictions — always  the  finest  test 
of  scientific  merit — stamps  Einstein  as  one  of 


From  Newton  to  Einstein  73 

those  super-men  who  from  time  to  time  are  sent 
to  us  to  give  us  a  peep  into  the  beyond. 

Some  Facts  about  Einstein  Himself.  Albert 
Einstein  was  born  in  Germany  some  45  years 
ago.  At  first  he  was  engaged  at  the  Patent 
Bureau  in  Berne,  and  later  became  professor  at 
the  Zurich  Polytechnic.  After  a  short  stay  at 
Prague  University  he  accepted  one  of  those  tempt- 
ing "Akademiker"  professorships  at  the  uni- 
versity of  Berlin — professorships  which  insure  a 
comfortable  income  to  the  recipient  of  one  of 
them,  little  university  work  beyond,  perhaps, 
one  lecture  a  week,  and  splendid  facilities  for 
research.  A  similar  inducement  enticed  the 
chemical  philosopher,  van  't  Hoff,  to  leave  his 
Amsterdam,  and  the  Swedes  came  perilously  near 
losing  their  most  illustrious  scientist,  Arrhenius. 

Einstein  published  his  first  paper  on  relativity 
in  1905,  when  not  more  than  30  years  old.  Of 
this  paper  Planck,  the  Nobel  Laureate  in  physics 
this  year,  has  offered  this  opinion:  "It  surpasses 
in  boldness  everything  previously  suggested  in 
speculative  natural  philosophy  and  even  in  the 
philosophical  theories  of  knowledge.  The  rev- 
olution introduced  into  the  physical  conceptions 
of  the  world  is  only  to  be  compared  in  extent 
and  depth  with  that  brought  about  by  the  in- 


74  From  Newton  to  Einstein 


(reduction  of  the  Copernican  system  of  the 
universe." 

Einstein  published  a  full  exposition  of  the  rel- 
ativity theory  in  1916. 

During  the  momentous  years  of  1914-19,  Ein- 
stein quietly  pursued  his  labors.  There  seems  to 
be  some  foundation  for  the  belief  that  the  ways  of 
the  German  High  Command  found  little  favor  in 
his  eyes.  At  any  rate,  he  was  not  one  of  the  forty 
professors  who  signed  the  famous  manifesto  extol- 
ling Germany's  aims.  "We  know  for  a  fact," 
writes  Dr.  O.  A.  Rankine,  of  the  Imperial  College 
of  Science  and  Technology,  London,  "that  Ein- 
stein never  was  employed  on  war  work.  What- 
ever may  have  been  Germany's  mistakes  in  other 
directions,  she  left  her  men  of  science  severely 
alone.  In  fact,  they  were  encouraged  to  continue 
in  their  normal  occupations.  Einstein  undoubt- 
edly received  a  large  measure  of  support  from  the 
Imperial  Government,  even  when  the  German 
armies  were  being  driven  back  across  Belgium." 

Quite  recently  (June,  1920)  the  Barnard  Medal 
of  Columbia  University  was  conferred  on  him  "in 
recognition  of  his  highly  original  and  fruitful 
development  of  the  fundamental  concepts  of 
physics  through  application  of  mathematics."  In 
acknowledging  the  honor,  Prof.  Einstein  wrote  to 


From  Newton  to  Einstein  75 

President  Butler  that  "...  quite  apart  from 
the  personal  satisfaction,  I  believe  I  may  regard 
your  decision  [to  confer  the  medal  upon  him] 
as  a  harbinger  of  a  better  time  in  which  a  sense  of 
international  solidarity  will  once  more  unite 
scholars  of  the  various  countries." 

REFERENCES 

For  those  lacking  all  astronomical  knowledge, 
an  excellent  plan  would  be  to  read  the  first  40 
pages  of  W.  H.  Snyder's  Everyday  Science  (Allyn 
and  Bacon),  in  which  may  be  found  a  clear  and 
simple  account  of  the  solar  system.  This  could 
be  followed  with  Bertrand  Russell's  chapter  on 
The  Nature  of  Matter  in  his  little  volume,  The 
Problems  of  Philosophy  (Henry  Holt  and  Co.). 
Here  the  reader  will  be  introduced  to  the  purely 
philosophical  side  of  the  question — quite  a  neces- 
sary equipment  for  the  understanding  of  Einstein's 
theory. 

Of  the  non-mathematical  articles  which  have 
appeared,  those  by  Prof.  A.  S.  Eddington  (Nature, 
volume  101,  pages  15  and  34,  1918)  and  Prof. 
M.  R.  Cohen  (The  New  Republic,  Jan.  21,  1920) 
are  the  best  which  have  come  to  the  author's 
notice.  Other  articles  on  Einstein's  theory,  some 
easily  comprehensible,  others  somewhat  con- 


76  From  Newton  to  Einstein 


fusing,  and  still  others  full  of  noise  and  rather 
empty,  are  by  H.  A.  Lorentz,  The  New  York  Times, 
Dec.  21,  1919  (since  reprinted  in  book  form  by 
Brentano's,  New  York,  1920);  J.  Q.  Stewart, 
Scientific  American,  Jan.  3,  1920;  E.  Cunningham, 
Nature,  volume  104,  pages  354  and  374,  1919;  F. 
H.  Loring,  Chemical  News,  volume  112,  pages  226, 
236,  248,  and  260,  1915;  E.  B.  Wilson,  Scientific 
Monthly,  volume  10,  page  217,  1920;  J.  S.  Ames, 
Science,  volume  51,  page  253,  1920*;  L.  A.  Bauer, 
Science,  volume  51,  page  301  (1920,  and  volume 
51,  page  581  (1920);  Sir  Oliver  Lodge,  Scientific 
Monthly,  volume  10,  page  378,  1920;  E.  E. 
Slosson,  Independent,  Nov.  29,  Dec.  13,  Dec.  20, 
Dec.  27,  1919  (since  collected  and  published  hi 
book  form  by  Harcourt,  Brace  and  Howe) ;  Isabel 
M.  Lewis,  Electrical  Experimenter,  Jan.,  1920; 
A.  J.  Lotka,  Harper's  Magazine,  March,  1920, 
page  477;  and  R.  D.  Carmichael,  New  York 
Times,  March  28,  1920.  Einstein  himself  is 
responsible  for  a  brief  article  in  English  which 
first  appeared  in  the  London  Times,  and  was 
later  reprinted  in  Science,  volume  51,  page  8,  1920 
(see  the  Appendix). 

A  number  of  books  deal  with  the  subject,  and 
all  of  them  are  more  or  less  mathematical.  How- 
ever, in  every  one  of  these  volumes  certain  chap- 

f  See  page  93. 


From  Newton  to  Einstein  77 

ters,  or  portions  of  chapters,  may  be  read  with 
profit  even  by  the  non-mathematical  reader. 
Some  of  these  books  are:  Erwin  Freundlich,  The 
Foundations  of  Einstein's  Theory  of  Gravitation 
(University  Press,  Cambridge,  1920).  (A  very 
complete  list  of  references — up  to  Feb.,  1920 — is 
also  given);  A.  S.  Eddington,  Report  on  the 
Relativity  Theory  of  Gravitation  for  the  Physical 
Society  of  London  (Fleetway  Press,  Ltd.,  Lon- 
don, 1920);  R.  C.  Tolman,  Theory  of  the  Relativity 
of  Motion  (University  of  California  Press,  1917); 
E.  Cunningham,  Relativity  and  the  Electron  Theory- 
(Longmans,  Green  and  Co.,  1915);  R.  D.  Car- 
michael,  The  Theory  of  Relativity  (John  Wiley  and 
Sons,  1913) ;  L.  Silberstein,  The  Theory  of  Rela- 
tivity (Macmillan,  1914);  and  E.  Cunningham, 
The  Principle  of  Relativity  (University  Press, 
Cambridge,  England,  1914). 

To  those  familiar  with  the  German  language 
Einstein's  book,  Ueber  die  spezielle  und  die  allge- 
meine  Relativitats-theorie  (Friedr.  Vieweg  und 
Sohn,  Braunschweig,  1920),  may  be  recom- 
mended.* 

The  mathematical  student  may  be  referred  to  a 

*  This  has  since  been  translated  into  English  by  Dr.  Law- 
son  and  published  by  Methuen  (London). 

Since  the  above  has  been  written  two  excellent  books  have 


78  From  Newton  to  Einstein 

volume  incorporating  the  more  important  papers 
of  Einstein,  Minkowski  and  Lorentz:  Das  Rela- 
tivitdtsprinzip,  (B.  G.  Teubner,  Berlin,  1913). 

Einstein's  papers  have  appeared  in  the  Annalen 
der  Physiky  Leipzig,  volume  17,  page  132,  1905, 
volume  49,  page  769,  1916,  and  volume  55,  page 
241,  1918. 

have  been  published.  One  is  by  Prof.  A.  S.  Eddington, 
Space,  Time  and  Gravitation  (Cambridge  Univ.  Press,  1920). 
The  other,  somewhat  more  of  a  philosophical  work,  is  Prof. 
Moritz  Schlick's  Space  and  Time  in  Contemporary  Physics 
(Oxford  Univ.  Press,  1920). 

Though  published  as  early  as  1897,  Bertrand  Russell's 
An  Essay  on  the  Foundations  of  Geometry  (Cambridge  Univ. 
Press,  1897)  contains  a  fine  account  of  non-Euclidean  geom- 
etry. 


APPENDIX 


APPENDIX 


NOTE  1  (page  21) 

"On  this  earth  there  is  indeed  a  tiny  corner  of  the  universe 
accessible  to  other  senses  [than  the  sense  of  sight] :  but  feeling 
and  taste  act  only  at  those  minute  distances  which  separate 
particles  of  matter  when  'in  contact:*  smell  ranges  over, 
at  the  utmost,  a  mile  or  two,  and  the  greatest  distance  which 
sound  is  ever  known  to  have  traveled  (when  Krakatoa 
exploded  in  1883)  is  but  a  few  thousand  miles — a  mere  fraction 
of  the  earth's  girdle." — Prof.  H.  H.  Turner  of  Oxford, 

NOTE  2  (page  27) 

Huyghens  and  Leibnitz  both  objected  to  Newton's  inverse 
square  law  because  it  postulated  "action  at  a  distance," 
— for  example,  the  attractive  force  of  the  sun  and  the  earth. 
This  desire  for  "continuity"  in  physical  laws  led  to  the 
supposition  of  an  "ether."  We  may  here  anticipate  and 
state  that  the  reason  which  prompted  Huyghens  to  object 
to  Newton's  law  led  Einstein  in  our  own  day  to  raise  objec- 
tions to  the  "ether"  theory.  "In  the  formulation  of  physical 
laws,  only  those  things  were  to  be  regarded  as  being  in  causal 
connection  which  were  capable  of  being  actually  observed." 
And  the  "ether"  has  not  been  "actually  observed." 

The  idea  of  "continuity"  implies  distances  between  adja- 
cent points  that  are  infinitesimal  in  extent;  hence  the  idea 
of  "continuity"  comes  in  direct  opposition  with  the  finite 
distances  of  Newton. 

81 


82  Appendix 


The  statement  relating  to  causal  connection — the  refusal 
to  accept  an  "ether"  as  an  absolute  base  of  reference — 
leads  to  the  principle  of  the  relativity  of  motion. 

NOTE  3  (page  30) 

Sir  Oliver  Lodge  goes  to  the  extreme  of  pinning  his  faith  in 
the  reality  of  this  ether  rather  than  in  that  of  matter.  Witness 
the  following  statement  he  made  recently  before  a  New 
York  audience: 

"To  my  mind  the  ether  of  space  is  a  substantial  reality 
with  extraordinarily  perfect  properties,  with  an  immense 
amount  of  energy  stored  up  in  it,  with  a  constitution  which 
we  must  discover,  but  a  substantial  reality  far  more  impres- 
sive than  that  of  matter.  Empty  space,  as  we  call  it,  is 
full  of  ether,  but  it  makes  no  appeal  to  our  senses.  The 
appearance  is  as  if  it  were  nothing.  It  is  the  most  important 
thing  in  the  material  universe.  I  believe  that  matter  is  a 
modification  of  ether,  a  very  porous  substance,  a  thing  more 
analogous  to  a  cobweb  or  the  Milky  Way  or  something 
very  slight  and  unsubstantial,  as  compared  to  ether." 

And  again : 

"The  properties  of  ether  seem  to  be  perfect.  Matter  is 
less  so;  it  has  friction  and  elasticity.  No  imperfection  has 
been  discovered  in  the  ether  space.  It  doesn't  wear  out; 
there  is  no  dissipation  of  energy;  there  is  no  friction.  Ether 
is  material,  yet  it  is  not  matter;  both  are  substantial  realities  in 
physics,  but  it  is  the  ether  of  space  that  holds  things  together 
and  acts  as  a  cement.  My  business  is  to  call  attention  to 
the  whole  world  of  etherealness  of  things,  and  I  have  made 
it  a  subject  of  thirty  years'  study,  but  we  must  admit  that 
there  is  no  getting  hold  of  ether  except  indirectly." 

"I  consider  the  ether  of  space,"  says  Lodge,  in  conclusion, 


Appendix  83 


"the  one  substantial  thing  in  the  universe."     And  Lodge  is 
certainly  entitled  to  his  opinion. 

NOTE  4  (page  51) 

For  the  benefit  of  those  readers  who  wish  to  gain  a  deeper 
insight  into  the  relativity  principle,  we  shall  here  discuss  it 
very  briefly. 

Newton  and  Galileo  had  developed  a  relativity  principle 
in  mechanics  which  may  be  stated  as  follows:  If  one  system 
of  reference  is  in  uniform  rectilinear  motion  with  respect 
to  another  system  of  reference,  then  whatever  physical  laws 
are  deduced  from  the  first  system  hold  true  for  the  second 
system.  The  two  systems  are  equivalent.  If  the  two  sys- 
tems be  represented  by  xyz  and  x'y'z' \  and  if  they  move  with 
the  velocity  of  v  along  the  x-axis  with  respect  to  one  another, 
then  the  two  systems  are  mathematically  related  thus: 

x'=x— vt,    y1 '  =y,    z'=z,    t'  =t,      ...     (1) 

and  this  immediately  provides  us  with  a  means  of  trans- 
forming the  laws  of  one  system  to  those  of  another. 

With  the  development  of  electrodynamics  (which  we  may 
call  electricity  in  motion)  difficulties  arose  which  equations 
in  mechanics  of  type  (1)  could  no  longer  solve.  These 
difficulties  merely  increased  when  Maxwell  showed  that 
light  must  be  regarded  as  an  electromagnetic  phenomenon. 
For  suppose  we  wish  to  investigate  the  motion  of  a  source 
of  light  (which  may  be  the  equivalent  of  the  motion  of  the 
earth  with  reference  to  the  sun)  with  respect  to  the  velocity 
of  the  light  it  emits — a  typical  example  of  the  study  of  moving 
systems — how  are  we  to  coordinate  the  electrodynamical 
and  mechanical  elements?  Or,  again,  suppose  we  wish  to 


84  Appendix 


investigate  the  velocity  of  electrons  shot  out  from  radium 
with  a  speed  comparable  to  that  of  light,  how  are  we  to 
coordinate  the  two  branches  in  tracing  the  course  of  these 
negative  particles  of  electricity? 

It  was  difficulties  such  as  these  that  led  to  the  Lorentz- 
Einstein  modifications  of  the  Newton-Galileo  relativity 
equations  (1).  The  Lorentz-Einstein  equations  are  expressed 
in  the  form: 


..     (2) 


c  denoting  the  velocity  of  light  in  vacuo  (which,  according  to 
all  observations,  is  the  same,  irrespective  of  the  observer's 
state  of  motion).  Here,  you  see,  electrodynamical  systems 
(light  and  therefore  "ray"  velocities  such  as  those  due  to 
electrons)  are  brought  into  play. 

This  gives  us  Einstein's  special  theory  of  relativity.  From 
it  Einstein  deduced  some  startling  conceptions  of  time  and 
space. 

NOTE  5  (page  55) 

The  velocity  (v)  of  an  object  in  one  system  will  have  a 
different  velocity  (v')  if  referred  to  another  system  in  uniform 
motion  relative  to  the  first.  It  had  been  supposed  that 
only  a  "something"  endowed  with  infinite  velocity  would 
show  the  same  velocity  in  all  systems,  irrespective  of  the 
motions  of  the  latter.  Michelson  and  Morley's  results 
actually  point  to  the  velocity  of  light  as  showing  the  proper- 
ties of  the  imaginary  "infinite  velocity."  The  velocity  of  light 
possesses  universal  significance;  and  this  is  the  basis  for 
much  of  Einstein's  earlier  work. 


Appendix  85 


NOTE  6  (page  56) 

"Euclid  assumes  that  parallel  lines  never  meet,  which  they 
cannot  do  of  course  if  they  be  defined  as  equidistant.  But  are 
there  such  lines?  And  if  not,  why  not  assume  that  all  lines 
drawn  through  a  point  outside  a  given  line  will  eventually 
intersect  it?  Such  an  assumption  leads  to  a  geometry  in 
which  all  lines  are  conceived  as  being  drawn  on  the  surface  of 
a  sphere  or  an  ellipse,  and  in  it  the  three  angles  of  a  triangle 
are  never  quite  equal  to  two  right  angles,  nor  the  circum- 
ference of  a  circle  quite  TT  times  its  diameter.  But  that  is  pre- 
cisely what  the  contraction  effect  due  to  motion  requires." 

(DR.  WALKER) 

NOTE  7  (page  57) 

Einstein  had  become  tired  of  assumptions.  He  had  no 
particular  objection  to  the  "ether"  theory  beyond  the  fact 
that  this  "ether"  did  not  come  within  the  range  of  our  senses; 
it  could  not  be  "observed."  "The  consistent  fulfilment  of 
the  two  postulates — *  action  by  contact'  and  causal  relation- 
ship between  only  such  things  as  lie  within  the  realm  of 
observation  [see  Note  2]  combined  together  is,  I  believe, 
the  mainspring  of  Einstein's  method  of  investigation  ..." 
(Prof.  Freundlich). 

NOTE  8  (page  59) 

That  the  conception  of  the  "simultaneity"  of  events  is 
devoid  of  meaning  can  be  deduced  from  equation  (2)  [see 
NOTE  4].  We  owe  the  proof  to  Einstein.  "It  is  possible  to 
select  a  suitable  time-coordinate  in  such  a  way  that  a  time- 
measurement  enters  into  physical  laws  in  exactly  the  same 
manner  as  regards  its  significance  as  a  space  measurement 
(that  is,  they  are  fully  equivalent  symbolically),  and  has 


Appendix 


likewise  a  definite  coordinate  direction  ...  It  never 
occurred  to  anyone  that  the  use  of  a  light-signal  as  a  means 
of  connection  between  the  moving-body  and  the  observer, 
which  is  necessary  in  practice  in  order  to  determine  simul- 
taneity, might  affect  the  final  result,  i.e.,  of  time  measurements 
in  different  systems."  (Freundlich).  But  that  is  just  what 
Einstein  shows,  because  time-measurements  are  based  on 
"simultaneity  of  events,"  and  this,  as  pointed  out  above, 
is  devoid  of  meaning. 

Had  the  older  masters  the  occasion  to  study  enormous 
velocities,  such  as  the  velocity  of  light,  rather  than  relatively 
small  ones — and  even  the  velocity  of  the  earth  around  the 
sun  is  small  as  compared  to  the  velocity  of  light — dis- 
crepancies between  theory  and  experiment  would  have 
become  apparent. 

NOTE  9  (page  67) 

How  the  special  theory  of  relativity  (see  Note  4)  led  to 
the  general  theory  of  relativity  (which  included  gravitation) 
may  now  be  briefly  traced. 

When  we  speak  of  electrons,  or  negative  particles  of  elec- 
tricity, in  motion,  we  are  speaking  of  energy  in  motion.  Now 
these  electrons  when  in  motion  exhibit  properties  that  are 
very  similar  to  matter  in  motion.  Whatever  deviations  there 
are  are  due  to  the  enormous  velocity  of  these  electrons, 
and  this  velocity,  as  has  already  been  pointed  out,  is  com- 
parable to  that  of  light;  whereas  before  the  advent  of  the 
electron,  the  velocity  of  no  particles  comparable  to  that  of 
light  had  ever  been  measured. 

According  to  present  views  "all  inertia  of  matter  consists 
only  of  the  inertia  of  the  latent  energy  in  it;  ...  every- 


Appendix  87 


thing  that  we  know  of  the  inertia  of  energy  holds  without 
exception  for  the  inertia  of  matter." 

Now  it  is  on  the  assumption  that  inertial  mass  and  gravi- 
tational "pull"  are  equivalent  that  the  mass  of  a  body  is 
determined  by  its  weight.  What  is  true  of  matter  should 
be  true  of  energy. 

The  special  theory  of  relativity,  however,  takes  into 
account  only  inertia  ("inertial  mass")  but  not  gravitation 
(gravitational  pull  or  weight)  of  energy.  When  a  body  absorbs 
energy  equation  2  (see  Note  4)  will  record  a  gain  in  inertia 
but  not  in  weight — which  is  contrary  to  one  of  the  funda- 
mental facts  in  mechanics. 

This  means  that  a  more  general  theory  of  relativity  is  re- 
quired to  include  gravitational  phenomena.  Hence  Einstein's 
General  Theory  of  Relativity.  Hence  the  approach  to  a  new 
theory  of  gravitation.  Hence  "the  setting  up  of  a  differential 
equation  which  comprises  the  motion  of  a  body  under  the 
influence  of  both  inertia  and  gravity,  and  which  symbolically 
expresses  the  relativity  of  motions  .  .  .  The  differential 
law  must  always  preserve  the  same  form,  irrespective  of 
the  sytem  of  coordinates  to  which  it  is  referred,  so  that 
no  system  of  coordinates  enjoys  a  preference  to  any  other." 
(For  the  general  form  of  the  equation  and  for  an  excellent 
discussion  of  its  significance,  see  Freundlich's  monograph, 
pages  27-33.) 


TIME,  SPACE  AND  GRAVITATION* 

BY 

PROF.  ALBERT  EINSTEIN 

THERE  are  several  kinds  of  theory  in  physics.  Most  of 
them  are  constructive.  These  attempt  to  build  a  picture  of 
complex  phenomena  out  of  some  relatively  simple  proposition. 
The  kinetic  theory  of  gases,  for  instance,  attempts  to  refer 
to  molecular  movement  the  mechanical  thermal,  and  dif- 
fusional  properties  of  gases.  When  we  say  that  we  under- 
stand a  group  of  natural  phenomena,  we  mean  that  we  have 
found  a  constructive  theory  which  embraces  them. 

Theories  of  Principle. — But  in  addition  to  this  most  weighty 
group  of  theories,  there  is  another  group  consisting  of  what  I 
call  theories  of  principle.  These  employ  the  analytic,  not 
the  synthetic  method.  Their  starting-point  and  foundation 
are  not  hypothetical  constituents,  but  empirically  observed 
general  properties  of  phenomena,  principles  from  which  math- 
ematical formulae  are  deduced  of  such  a  kind  that  they  apply 
to  every  case  which  presents  itself.  Thermodynamics,  for 
instance,  starting  from  the  fact  that  perpetual  motion  never 
occurs  in  ordinary  experience,  attempts  to  deduce  from  this, 
by  analytic  processes,  a  theory  which  will  apply  in  every  case. 
The  merit  of  constructive  theories  is  their  comprehensiveness, 
adaptability,  and  clarity,  that  of  the  theories  of  principle, 
their  logical  perfection,  and  the  security  of  their  foundation. 

The  theory  of  relativity  is  a  theory  of  principle.  To  under- 
stand it,  the  principles  on  which  it  rests  must  be  grasped. 
But  before  stating  these  it  is  necessary  to  point  out  that 
the  theory  of  relativity  is  like  a  house  with  two  separate 

*  Republished  by  permission  from  "Science." 
88 


Appendix 


stories,  the  special  relativity  theory  and  the  general  theory 
of  relativity. 

Since  the  time  of  the  ancient  Greeks  it  has  been  well  known 
that  in  describing  the  motion  of  a  body  we  must  refer  to 
another  body.  The  motion  of  a  railway  train  is  described 
with  reference  to  the  ground,  of  a  planet  with  reference  to 
the  total  assemblage  of  visible  fixed  stars.  In  physics  the 
bodies  to  which  motions  are  spatially  referred  are  termed 
systems  of  coordinates.  The  laws  of  mechanics  of  Galileo 
and  Newton  can  be  formulated  only  by  using  a  system  of 
coordinates. 

The  state  of  motion  of  a  system  of  coordinates  can  not  be 
chosen  arbitrarily  if  the  laws  of  mechanics  are  to  hold  good 
(it  must  be  free  from  twisting  and  from  acceleration).  The 
system  of  coordinates  employed  in  mechanics  is  called  an 
inertia-system.  The  state  of  motion  of  an  inertia-system, 
so  far  as  mechanics  are  concerned,  is  not  restricted  by  nature 
to  one  condition.  The  condition  in  the  following  proposition 
suffices;  a  system  of  coordinates  moving  in  the  same  direction 
and  at  the  same  rate  as  a  system  of  inertia  is  itself  a  system  of 
inertia.  The  special  relativity  theory  is  therefore  the  appli- 
cation of  the  following  proposition  to  any  natural  process: 
"Every  law  of  nature  which  holds  good  with  respect  to  a 
coordinate  system  K  must  also  hold  good  for  any  other  system 
Kf  provided  that  K  and  K'  are  in  uniform  movement  of  trans- 
lation." 

The  second  principle  on  which  the  special  relativity  theory 
rests  is  that  of  the  constancy  of  the  velocity  of  light  in  a  vac- 
uum. Light  in  a  vacuum  has  a  definite  and  constant  velocity, 
independent  of  the  velocity  of  its  source.  Physicists  owe 
their  confidence  in  this  proposition  to  the  Maxwell-Lorentz 
theory  of  electro-dynamics. 


90  Appendix 


The  two  principles  which  I  have  mentioned  have  received 
strong  experimental  confirmation,  but  do  not  seem  to  be 
logically  compatible.  The  special  relativity  theory  achieved 
their  logical  reconciliation  by  making  a  change  in  kinematics, 
that  is  to  say,  in  the  doctrine  of  the  physical  laws  of  space  and 
time.  It  became  evident  that  a  statement  of  the  coincidence 
of  two  events  could  have  a  meaning  only  in  connection  with  a 
system  of  coordinates,  that  the  mass  of  bodies  and  the  rate  of 
movement  of  clocks  must  depend  on  their  state  of  motion 
with  regard  to  the  coordinates. 

The  Older  Physics. — But  the  older  physics,  including  the 
laws  of  motion  of  Galileo  and  Newton,  clashed  with  the 
relativistic  kinematics  that  I  have  indicated.  The  latter  gave 
origin  to  certain  generalized  mathematical  conditions  with 
which  the  laws  of  nature  would  have  to  conform  if  the  two 
fundamental  principles  were  compatible.  Physics  had  to  be 
modified.  The  most  notable  change  was  a  new  law  of  motion 
for  (very  rapidly)  moving  mass-points,  and  this  soon  came 
to  be  verified  in  the  case  of  electrically-laden  particles.  The 
most  important  result  of  the  special  relativity  system  con- 
cerned the  inert  mass  of  a  material  system.  It  became  evident 
that  the  inertia  of  such  a  system  must  depend  on  its  energy- 
content,  so  that  we  were  driven  to  the  conception  that  inert 
mass  was  nothing  else  than  latent  energy.  The  doctrine 
of  the  conservation  of  mass  lost  its  independence  and  became 
merged  in  the  doctrine  of  conservation  of  energy. 

The  special  relativity  theory  which  was  simply  a  systematic 
extension  of  the  electro-dynamics  of  Maxwell  and  Lorentz, 
had  consequences  which  reached  beyond  itself.  Must  the 
independence  of  physical  laws  with  regard  to  a  system  of 
coordinates  be  limited  to  systems  of  coordinates  in  uniform 
movement  of  translation  with  regard  to  one  another?  What 


Appendix 


has  nature  to  do  with  the  coordinate  systems  that  we  pro- 
pose and  with  their  motions?  Although  it  may  be  necessary 
for  our  descriptions  of  nature  to  employ  systems  of  coordinates 
that  we  have  selected  arbitrarily,  the  choice  should  not  be 
limited  in  any  way  so  far  as  their  state  of  motion  is  concerned. 
(General  theory  of  relativity.)  The  application  of  this  gen- 
eral theory  of  relativity  was  found  to  be  in  conflict  with  a 
well-known  experiment,  according  to  which  it  appeared  that 
the  weight  and  the  inertia  of  a  body  depended  on  the  same 
constants  (identity  of  inert  and  heavy  masses).  Consider 
the  case  of  a  system  of  coordinates  which  is  conceived  as  being 
in  stable  rotation  relative  to  a  system  of  inertia  in  the  New- 
tonian sense.  The  forces  which,  relatively  to  this  system,  are 
centrifugal  must,  in  the  Newtonian  sense,  be  attributed  to 
inertia.  But  these  centrifugal  forces  are,  like  gravitation, 
proportional  to  the  mass  of  the  bodies.  Is  it  not,  then,  pos- 
sible to  regard  the  system  of  coordinates  as  at  rest,  and  the 
centrifugal  forces  as  gravitational?  The  interpretation  seemed 
obvious,  but  classical  mechanics  forbade  it. 

This  slight  sketch  indicates  how  a  generalized  theory  of 
relativity  must  include  the  laws  of  gravitation,  and  actual 
pursuit  of  the  conception  has  justified  the  hope.  But  the 
way  was  harder  than  was  expected,  because  it  contradicted 
Euclidian  geometry.  In  other  words,  the  laws  according  to 
which  material  bodies  are  arranged  in  space  do  not  exactly 
agree  with  the  laws  of  space  prescribed  by  the  Euclidian 
geometry  of  solids.  This  is  what  is  meant  by  the  phrase  "a 
warp  in  space."  The  fundamental  concepts  "straight," 
"plane,"  etc.,  accordingly  lose  their  exact  meaning  in  physics. 

In  the  generalized  theory  of  relativity,  the  doctrine  of  space 
and  time,  kinematics,  is  no  longer  one  of  the  absolute  founda- 
tions of  general  physics.  The  geometrical  states  of  bodies 


92  Appendix 


and  the  rates  of  clocks  depend  in  the  first  place  on  their  gravi- 
tational fields,  which  again  are  produced  by  the  material  system 
concerned. 

Thus  the  new  theory  of  gravitation  diverges  widely  from 
that  of  Newton  with  respect  to  its  basal  principle.  But  in 
practical  application  the  two  agree  so  closely  that  it  has  been 
difficult  to  find  cases  in  which  the  actual  differences  could  be 
subjected  to  observation.  As  yet  only  the  following  have 
been  suggested: 

1.  The  distortion  of  the  oval  orbits  of  planets  round  the  sun 
(confirmed  in  the  case  of  the  planet  Mercury). 

2.  The  deviation  of  light-rays  in  a  gravitational  field  (con- 
firmed by  the  English  Solar  Eclipse  expedition). 

3.  The  shifting  of  spectral  lines  towards  the  red  end  of  the 
spectrum  in  the  case  of  light  coming  to  us  from  stars  of  appre- 
ciable mass  (not  yet  confirmed). 

The  great  attraction  of  the  theory  is  its  logical  consistency. 
If  any  deduction  from  it  should  prove  untenable,  it  must  be 
given  up.  A  modification  of  it  seems  impossible  without 
destruction  of  the  whole. 

No  one  must  think  that  Newton's  great  creation  can  be 
overthrown  in  any  real  sense  by  this  or  by  any  other  theory. 
His  clear  and  wide  ideas  will  for  ever  retain  their  significance 
as  the  foundation  on  which  our  modern  conceptions  of  physics 
have  been  built. 


Appendix  93 


EINSTEIN'S  LAW  OF  GRAVITATION* 

BT 

PROF.  J.  S.  AMES 
Johns  Hopkins  University 

...  IN  the  treatment  of  Maxwell's  equations  of  the  electro- 
magnetic field,  several  investigators  realized  the  importance 
of  deducing  the  form  of  the  equations  when  applied  to  a 
system  moving  with  a  uniform  velocity.  One  object  of  such 
an  investigation  would  be  to  determine  such  a  set  of  trans- 
formation formulae  as  would  leave  the  mathematical  form 
of  the  equations  unaltered.  The  necessary  relations  between 
the  new  space-coordinates,  those  applying  to  the  moving 
system,  and  the  original  set  were  of  course  obvious;  and  ele- 
mentary methods  led  to  the  deduction  of  a  new  variable  which 
should  replace  the  time  coordinate.  This  step  was  taken  by 
Lorentz  and  also,  I  believe,  by  Larmor  and  by  Voigt.  The 
mathematical  deductions  and  applications  in  the  hands  of 
these  men  were  extremely  beautiful,  and  are  probably  well 
known  to  you  all. 

Lorentz'  paper  on  this  subject  appeared  in  the  Proceedings 
of  the  Amsterdam  Academy  in  1904.  In  the  following  year 
there  was  published  in  the  Annalen  der  Physik  a  paper  by 
Einstein,  written  without  any  knowledge  of  the  work  of 
Lorentz,  in  which  he  arrived  at  the  same  transformation 
equations  as  did  the  latter,  but  with  an  entirely  different  and 
fundamentally  new  interpretation.  Einstein  called  atten-^ 
tion  in  his  paper  to  the  lack  of  definiteness  in  the  concepts 
of  time  and  space,  as  ordinarily  stated  and  used.  He  analyzed 
clearly  the  definitions  and  postulates  which  were  necessary 

*  Presidential  address  delivered  at  the  St.  Louis  meeting  of  the 
Physical  Society,  December  30,  1919.  Republished  by  permis- 
sion from  "  Science." 


94  Appendix 


before  one  could  speak  with  exactness  of  a  length  or  of  an 
interval  of  time.  He  disposed  forever  of  the  propriety  of*' 
speaking  of  the  "true'*  length  of  a  rod  or  of  the  "true" 
duration  of  time,  showing,  in  fact,  that  the  numerical  values 
which  we  attach  to  lengths  or  intervals  of  time  depend  upon 
the  definitions  and  postulates  which  we  adopt.  The  words 
"absolute"  space  or  time  intervals  are  devoid  of  meaning. 
As  an  illustration  of  what  is  meant  Einstein  discussed  two 
possible  ways  of  measuring  the  length  of  a  rod  when  it  is 
moving  in  the  direction  of  its  own  length  with  a  uniform 
velocity,  that  is,  after  having  adopted  a  scale  of  length,  two 
ways  of  assigning  a  number  to  the  length  of  the  rod  con- 
cerned. One  method  is  to  imagine  the  observer  moving  with 
the  rod,  applying  along  its  length  the  measuring  scale,  and 
reading  off  the  positions  of  the  ends  of  the  rod.  Another 
method  would  be  to  have  two  observers  at  rest  on  the  body 
with  reference  to  which  the  rod  has  the  uniform  velocity,  so 
stationed  along  the  line  of  motion  of  the  rod  that  as  the  rod 
moves  past  them  they  can  note  simultaneously  on  a  stationary 
measuring  scale  the  positions  of  the  two  ends  of  the  rod. 
Einstein  showed  that,  accepting  two  postulates  which  need 
no  defense  at  this  time,  the  two  methods  of  measurements 
would  lead  to  different  numerical  values,  and,  further,  that 
the  divergence  of  the  two  results  would  increase  as  the  velocity 
of  the  rod  was  increased.  In  assigning  a  number,  therefore, 
to  the  length  of  a  moving  rod,  one  must  make  a  choice  of  the 
method  to  be  used  in  measuring  it.  Obviously  the  preferable 
method  is  to  agree  that  the  observer  shall  move  with  the  rod, 
carrying  his  measuring  instrument  with  him.  This  disposes 
of  the  problem  of  measuring  space  relations.  The  observed 
fact  that,  if  we  measure  the  length  of  the  rod  on  different 
days,  or  when  the  rod  is  lying  in  different  positions,  we  always 


Appendix  95 


obtain  the  same  value  offers  no  information  concerning  the 
"real "  length  of  the  rod.  It  may  have  changed,  or  it  may  not. 
It  must  always  be  remembered  that  measurement  of  the 
length  of  a  rod  is  simply  a  process  of  comparison  between  it 
and  an  arbitrary  standard,  e.g.,  a  meter-rod  or  yard-stick. 
In  regard  to  the  problem  of  assigning  numbers  to  intervals  of 
time,  it  must  be  borne  in  mind  that,  strictly  speaking,  we  do 
not  "measure"  such  intervals,  i.e.,  that  we  do  not  select  a 
unit  interval  of  time  and  find  how  many  times  it  is  contained 
in  the  interval  in  question.  (Similarly,  we  do  not  "measure" 
the  pitch  of  a  sound  or  the  temperature  of  a  room.)  Our 
practical  instruments  for  assigning  numbers  to  time-inter- 
vals depend  in  the  main  upon  our  agreeing  to  believe  that  a 
pendulum  swings  in  a  perfectly  uniform  manner,  each  vibra- 
tion taking  the  same  time  as  the  next  one.  Of  course  we 
cannot  prove  that  this  is  true,  it  is,  strictly  speaking,  a  defini- 
tion of  what  we  mean  by  equal  intervals  of  time;  and  it  is 
not  a  particularly  good  definition  at  that.  Its  limitations  are 
sufficiently  obvious.  The  best  way  to  proceed  is  to  consider 
the  concept  of  uniform  velocity,  and  then,  using  the  idea 
of  some  entity  having  such  a  uniform  velocity,  to  define  equal 
intervals  of  time  as  such  intervals  as  are  required  for  the  entity 
to  traverse  equal  lengths.  These  last  we  have  already  defined. 
What  is  required  in  addition  is  to  adopt  some  moving  entity 
as  giving  our  definition  of  uniform  velocity.  Considering 
our  known  universe  it  is  self-evident  that  we  should  choose 

our  definition  of  uniform  velocity  the  velocity  of  light,  since 
is  selection  could  be  made  by  an  observer  anywhere  in  our 

i verse.  Having  agreed  then  to  illustrate  by  the  words 
"uniform  velocity"  that  of  light,  our  definition  of  equal  inter- 
vals of  time  is  complete.  This  implies,  of  course,  that  there  is 

uncertainty  on  our  part  as  to  the  fact  that  the  velocity  of 


96  Appendix 


light  always  has  the  same  value  at  any  one  point  in  the  uni- 
verse to  any  observer,  quite  regardless  of  the  source  of  light. 
In  other  words,  the  postulate  that  this  is  true  underlies  our 
definition.  Following  this  method  Einstein  developed  a 
system  of  measuring  both  space  and  time  intervals.  As  a 
matter  of  fact  his  system  is  identically  that  which  we  use  in 
daily  life  with  reference  to  events  here  on  the  earth.  He 
further  showed  that  if  a  man  were  to  measure  the  length 
of  a  rod,  for  instance,  on  the  earth  and  then  were  able  to  carry 
the  rod  and  his  measuring  apparatus  to  Mars,  the  sun,  or  to 
Arcturus  he  would  obtain  the  same  numerical  value  for  the 
length  in  all  places  and  at  all  times.  This  doesn't  mean  that 
any  statement  is  implied  as  to  whether  the  length  of  the  rod 
has  remained  unchanged  or  not;  such  words  do  not  have  any 
meaning — remember  that  we  can  not  speak  of  true  length. 
It  is  thus  clear  that  an  observer  living  on  the  earth  would  have 
a  definite  system  of  units  in  terms  of  which  to  express  space 
and  time  intervals,  i.e.,  he  would  have  a  definite  system  of 
space  coordinates  (x,  y,  z)  and  a  definite  time  coordinate  (t) ; 
and  similarly  an  observer  living  on  Mars  would  have  his 
system  of  coordinates  (#',  y',  z',  t').  Provided  that  one 
observer  has  a  definite  uniform  velocity  with  reference  to  the 
other,  it  is  a  comparatively  simple  matter  to  deduce  the 
mathematical  relations  between  the  two  sets  of  coordinates. 
When  Einstein  did  this,  he  arrived  at  the  same  transformation 
formulae  as  those  used  by  Lorentz  in  his  development  of 
Maxwell's  equations.  The  latter  had  shown  that,  using  these 
formulae,  the  form  of  the  laws  for  all  electromagnetic  phe- 
nomena maintained  the  same  form;  so  Einstein's  method 
J  proves  that  using  his  system  of  measurement  an  observer, 
anywhere  in  the  universe,  would  as  the  result  of  his  own 
investigation  of  electromagnetic  phenomena  arrive  at  the 


Appendix  97 


same  mathematical  statement  of  them  as  any  other  observer, 
provided  only  that  the  relative- velocity  of  the  two  observers 
was  uniform. 

Einstein  discussed  many  other  most  important  questions 
at  this  time;  but  it  is  not  necessary  to  refer  to  them  in  con- 
nection with  the  present  subject.  So  far  as  this  is  concerned, 
the  next  important  step  to  note  is  that  taken  in  the  famous 
address  of  Minkowski,  in  1908,  on  the  subject  of  "Space  and 
Time."  It  would  be  difficult  to  overstate  the  importance  of 
the  concepts  advanced  by  Minkowski.  They  marked  the  ' 
beginning  of  a  new  period  in  the  philosophy  of  physics.  I 
shall  not  attempt  to  explain  his  ideas  in  detail,  but  shall 
confine  myself  to  a  few  general  statements.  His  point  of  view 
and  his  line  of  development  of  the  theme  are  absolutely  dif- 
ferent from  those  of  Lorentz  or  of  Einstein;  but  in  the  end 
he  makes  use  of  the  same  transformation  formulae.  His 
great  contribution  consists  in  giving  us  a  new  geometrical 
picture  of  their  meaning.  It  is  scarcely  fair  to  call  Minkowski's 
development  a  picture;  for  to  us  a  picture  can  never  have 
more  than  three  dimensions,  our  senses  limit  us;  while  his 
picture  calls  for  perception  of  four  dimensions.  It  is  this  fact 
that  renders  any  even  semi-popular  discussion  of  Minkowski's 
work  so  impossible.  We  can  all  see  that  for  us  to  describe 
any  event  a  knowledge  of  four  coordinates  is  necessary,  three 
for  the  space  specification  and  one  for  the  time.  A  com- 
plete picture  could  be  given  then  by  a  point  in  four  dimen- 
sions. All  four  coordinates  are  necessary:  we  never  observe 
an  event  except  at  a  certain  time,  and  we  never  observe  an 
instant  of  time  except  with  reference  to  space.  Discussing 
the  laws  of  electromagnetic  phenomena,  Minkowski  showed 
how  in  a  space  of  four  dimensions,  by  a  suitable  definition  of 
axes,  the  mathematical  transformation  of  Lorentz  and  Ein- 


98  Appendix 


stein  could  be  described  by  a  rotation  of  the  set  of  axes.  We 
are  all  accustomed  to  a  rotation  of  our  ordinary  cartesian 
set  of  axes  describing  the  position  of  a  point.  We  ordinarily 
choose  our  axes  at  any  location  on  the  earth  as  follows:  one 
vertical,  one  east  and  west,  one  north  and  south.  So  if  we 
move  from  any  one  laboratory  to  another,  we  change  our  axes; 
they  are  always  orthogonal,  but  in  moving  from  place  to  place 
there  is  a  rotation.  Similarly,  Minkowski  showed  that  if  we 
choose  four  orthogonal  axes  at  any  point  on  the  earth,  accord- 
ing to  his  method,  to  represent  a  space-time  point  using  the 
method  of  measuring  space  and  time  intervals  as  outlined  by 
Einstein;  and,  if  an  observer  on  Arcturus  used  a  similar  set 
of  axes  and  the  method  of  measurement  which  he  naturally 
would,  the  set  of  axes  of  the  latter  could  be  obtained  from  those 
of  the  observer  on  the  earth  by  a  pure  rotation  (and  naturally 
a  transfer  of  the  origin) .  This  is  a  beautiful  geometrical  result. 
To  complete  my  statement  of  the  method,  I  must  add  that 
instead  of  using  as  his  fourth  axis  one  along  which  numerical 
values  of  time  are  laid  off,  Minkowski  defined  his  fourth 
coordinate  as  the  product  of  time  and  the  imaginary  constant, 
the  square  root  of  minus  one.  This  introduction  of  imaginary 
quantities  might  be  expected,  possibly,  to  introduce  difficul- 
ties; but,  in  reality,  it  is  the  very  essence  of  the  simplicity  of 
the  geometrical  description  just  given  of  the  rotation  of  the 
sets  of  axes.  It  thus  appears  that  different  observers  situated 
at  different  points  in  the  universe  would  each  have  their  own 
set  of  axes,  all  different,  yet  all  connected  by  the  fact  that 
any  one  can  be  rotated  so  as  to  coincide  with  any  other. 
This  means  that  there  is  no  one  direction  in  the  four-dimen- 
sional space  that  corresponds  to  time  for  all  observers.  Just 
as  with  reference  to  the  earth  there  is  no  direction  which  can 
be  called  vertical  for  all  observers  living  on  the  earth.  In  the 


Appendix  99 


sense  of  an  absolute  meaning  the  words  "up  and  down," 
"before  and  after,"  "sooner  or  later,"  are  entirely  meaning- 
less. 

This  concept  of  Minkowski's  may  be  made  clearer,  perhaps, 
by  the  following  process  of  thought.  If  we  take  a  section 
through  our  three-dimensional  space,  we  have  a  plane,  i.e., 
a  two-dimensional  space.  Similarly,  if  a  section  is  made 
through  a  four-dimensional  space,  one  of  three  dimensions  is 
obtained.  Thus,  for  an  observer  on  the  earth  a  definite 
section  of  Minkowski's  four-dimensional  space  will  give  us  our 
ordinary  three-dimensional  one;  so  that  this  section  will,  as  it 
were,  break  up  Minkowski's  space  into  our  space  and  give  us 
our  ordinary  time.  Similarly,  a  different  section  would  have 
to  be  used  to  the  observer  on  Arcturus;  but  by  a  suitable 
selection  he  would  get  his  own  familiar  three-dimensional 
space  and  his  own  time.  Thus  the  space  defined  by  Min- 
kowski  is  completely  isotropic  in  reference  to  measured  lengths 
and  times,  there  is  absolutely  no  difference  between  any  two 
directions  in  an  absolute  sense;  for  any  particular  observer,  of 
course,  a  particular  section  will  cause  the  space  to  fall  apart 
so  as  to  suit  his  habits  of  measurement;  any  section,  however, 
taken  at  random  will  do  the  same  thing  for  some  observer 
somewhere.  From  another  point  of  view,  that  of  Lorentz 
and  Einstein,  it  is  obvious  that,  since  this  four-dimensional 
space  is  isotropic,  the  expression  of  the  laws  of  electromagnetic 
phenomena  take  identical  mathematical  forms  when  expressed 
by  any  observer. 

The  question  of  course  must  be  raised  as  to  what  can  be 
said  in  regard  to  phenomena  which  so  far  as  we  know  do  not 
have  an  electromagnetic  origin.  In  particular  what  can  be 
done  with  respect  to  gravitational  phenomena?  Before,  how- 
ever, showing  how  this  problem  was  attacked  by  Einstein; 


100  Appendix 


and  the  fact  that  the  subject  of  my  address  is  Einstein's 
work  on  gravitation  shows  that  ultimately  I  shall  explain  this, 
I  must  emphasize  another  feature  of  Minkowski's  geometry. 
To  describe  the  space-time  characteristics  of  any  event  a 
point,  defined  by  its  four  coordinates,  is  sufficient;  so,  if  one 
observes  the  life-history  of  any  entity,  e.g.,  a  particle  of  matter, 
a  light- wave,  etc.,  he  observes  a  sequence  of  points  in  the  space- 
time  continuum;  that  is,  the  life-history  of  any  entity  is 
described  fully  by  a  line  in  this  space.  Such  a  line  was  called 
by  Minkowski  a  "world-line."  Further,  from  a  different  point 
of  view,  all  of  our  observations  of  nature  are  in  reality  obser- 
vations of  coincidences,  e.g.,  if  one  reads  a  thermometer,  what 
he  does  is  to  note  the  coincidence  of  the  end  of  the  column  of 
mercury  with  a  certain  scale  division  on  the  thermometer 
tube.  In  other  words,  thinking  of  the  world-line  of  the  end 
of  the  mercury  column  and  the  world-line  of  the  scale  division, 
what  we  have  observed  was  the  intersection  or  crossing  of 
these  lines.  In  a  similar  manner  any  observation  may  be 
analyzed;  and  remembering  that  light  rays,  a  point  on  the 
retina  of  the  eye,  etc.,  all  have  their  world-lines,  it  will  be  recog- 
nized that  it  is  a  perfectly  accurate  statement  to  say  that 
every  observation  is  the  perception  of  the  intersection  of  world- 
lines.  Further,  since  all  we  know  of  a  world-line  is  the  result 
of  observations,  it  is  evident  that  we  do  not  know  a  world- 
line  as  a  continuous  series  of  points,  but  simply  as  a  series  of 
discontinuous  points,  each  point  being  where  the  particular 
world-line  in  question  is  crossed  by  another  world-line. 

It  is  clear,  moreover,  that  for  the  description  of  a  world-line 
we  are  not  limited  to  the  particular  set  of  four  orthogonal  axes 
adopted  by  Minkowski.  We  can  choose  any  set  of  four- 
dimensional  axes  we  wrish.  It  is  further  evident  that  the 
mathematical  expression  for  the  coincidence  of  two  points  is 


- 


Appendix  101 


absolutely  independent  of  our  selection  of  reference  axes.  If 
we  change  our  axes,  we  will  change  the  coordinates  of  both 
points  simultaneously,  so  that  the  question  of  axes  ceases  to  be 
of  interest.  But  our  so-called  laws  of  nature  are  nothing  but 
descriptions  in  mathematical  language  of  our  observations; 
we  observe  only  coincidences;  a  sequence  of  coincidences  when 
put  in  mathematical  terms  takes  a  form  which  is  independent 
of  the  selection  of  reference  axes;  therefore  the  mathematical 
expression  of  our  laws  of  nature,  of  every  character,  must 
be  such  that  their  form  does  not  change  if  we  make  a  trans- 
formation of  axes.  This  is  a  simple  but  far-reaching  de- 
duction. 

There  is  a  geometrical  method  of  picturing  the  effect  of  a 
change  of  axes  of  reference,  i.e.,  of  a  mathematical  transforma- 
tion. To  a  man  in  a  railway  coach  the  path  of  a  drop  of  water 
does  not  appear  vertical,  i.e.,  it  is  not  parallel  to  the  edge  of 
the  window;  still  less  so  does  it  appear  vertical  to  a  man  per- 
forming manoeuvres  in  an  airplane.  This  means  that  whereas 
with  reference  to  axes  fixed  to  the  earth  the  path  of  the  drop  is 
vertical;  with  reference  to  other  axes,  the  path  is  not.  Or, 
stating  the  conclusion  in  general  language,  changing  the  axes 
of  reference  (or  effecting  a  mathematical  transformation)  in 
general  changes  the  shape  of  any  line.  If  one  imagines  the 
line  forming  a  part  of  the  space,  it  is  evident  that  if  the  space  is 
deformed  by  compression  or  expansion  the  shape  of  the  line 
is  changed,  and  if  sufficient  care  is  taken  it  is  clearly  possible, 
by  deforming  the  space,  to  make  the  line  take  any  shape 
desired,  or  better  stated,  any  shape  specified  by  the  previous 
change  of  axes.  It  is  thus  possible  to  picture  a  mathematical 
transformation  as  a  deformation  of  space.  Thus  I  can  draw  a 
line  on  a  sheet  of  paper  or  of  rubber  and  by  bending  and 
stretching  the  sheet,  I  can  make  the  line  assume  a  great  variety 


Appendix 


of  shapes;  each  of  these  new  shapes  is  a  picture  of  a  suitable 
transformation. 

Now,  consider  world-lines  in  our  four-dimensional  space. 
The  complete  record  of  all  our  knowledge  is  a  series  of  se- 
quences of  intersections  of  such  lines.  By  analogy  I  can  draw 
in  ordinary  space  a  great  number  of  intersecting  lines  on  a  sheet 
of  rubber;  I  can  then  bend  and  deform  the  sheet  to  please 
myself;  by  so  doing  I  do  not  introduce  any  new  intersections 
nor  do  I  alter  in  the  least  the  sequence  of  intersections.  So 
in  the  space  of  our  world-lines,  the  space  may  be  deformed  in 
any  imaginable  manner  without  introducing  any  new  inter- 
sections or  changing  the  sequence  of  the  existing  intersections. 
It  is  this  sequence  which  gives  us  the  mathematical  expression 
of  our  so-called  experimental  laws;  a  deformation  of  our  space 
is  equivalent  mathematically  to  a  transformation  of  axes, 
consequently  we  see  why  it  is  that  the  form  of  our  laws  must 
be  the  same  when  referred  to  any  and  all  sets  of  axes, 
that  is,  must  remain  unaltered  by  any  mathematical  trans- 
formation. 

Now,  at  last  we  come  to  gravitation.  We  can  not  imagine 
any  world-line  simpler  than  that  of  a  particle  of  matter  left 
to  itself;  we  shall  therefore  call  it  a  "straight"  line.  Our 
experience  is  that  two  particles  of  matter  attract  one  another 
Expressed  in  terms  of  world-lines,  this  means  that,  if  the  world- 
lines  of  two  isolated  particles  come  near  each  other,  the  lines, 
instead  of  being  straight,  will  be  deflected  or  bent  in  towards 
each  other.  The  world-line  of  any  one  particle  is  therefore 
deformed;  and  we  have  just  seen  that  a  deformation  is  the 
equivalent  of  a  mathematical  transformation.  In  other  words, 
for  any  one  particle  it  is  possible  to  replace  the  effect  of  a 
gravitational  field  at  any  instant  by  a  mathematical  transfor- 
mation of  axes.  The  statement  that  this  is  always  possible 


Appendix  103 


for  any  particle  at  any  instant  is  Einstein's  famous  "Principle 
of  Equivalence." 

Let  us  rest  for  a  moment,  while  I  call  attention  to  a  most 
interesting  coincidence,  not  to  be  thought  of  as  an  intersection 
of  world-lines .  It  is  said  that  Newton' s  thoughts  were  directed 
to  the  observation  of  gravitational  phenomena  by  an  apple 
falling  on  his  head;  from  this  striking  event  he  passed  by 
natural  steps  to  a  consideration  of  the  universality  of  gravita- 
tion. Einstein  in  describing  his  mental  process  in  the  evolu- 
tion of  his  law  of  gravitation  says  that  his  attention  was  called 
to  a  new  point  of  view  by  discussing  his  experiences  with  a 
man  whose  fall  from  a  high  building  he  had  just  witnessed. 
The  man  fortunately  suffered  no  serious  injuries  and  assured 
Einstein  that  in  the  course  of  his  fall  he  had  not  been  conscious 
in  the  least  of  any  pull  downward  on  his  body.  In  mathe- 
matical language,  with  reference  to  axes  moving  with  the 
man  the  force  of  gravity  had  disappeared.  This  is  a  case 
where  by  the  transfer  of  the  axes  from  the  earth  itself  to  the 
man,  the  force  of  the  gravitational  field  is  annulled.  The 
converse  change  of  axes  from  the  falling  man  to  a  point  on  the 
earth  could  be  considered  as  introducing  the  force  of  gravity 
into  the  equations  of  motion.  Another  illustration  of  the 
introduction  into  our  equations  of  a  force  by  a  means  of  a 
change  of  axes  is  furnished  by  the  ordinary  treatment  of  a 
body  in  uniform  rotation  about  an  axis.  For  instance,  in  the 
case  of  a  so-called  conical  pendulum,  that  is,  the  motion  of  a 
bob  suspended  from  a  fixed  point  by  string,  which  is  so  set 
in  motion  that  the  bob  describes  a  horizontal  circle  and  the 
string  therefore  describes  a  circular  cone,  if  we  transfer  our 
axes  from  the  earth  and  have  them  rotate  around  the  vertical 
line  through  the  fixed  point  with  the  same  angular  velocity  as 
the  bob,  it  is  necessary  to  introduce  into  our  equations  of 


104  Appendix 


motion  a  fictitious  "force"  called  the  centrifugal  force.  No 
one  ever  thinks  of  this  force  other  than  as  a  mathematical 
quantity  introduced  into  the  equations  for  the  sake  of  sim- 
plicity of  treatment;  no  physical  meaning  is  attached  to  it. 
Why  should  there  be  to  any  other  so-called  "force,"  which 
like  centrifugal  force,  is  independent  of  the  nature  of  the 
matter?  Again,  here  on  the  earth  our  sensation  of  weight  is 
interpreted  mathematically  by  combining  expressions  for 
centrifugal  force  and  gravity;  we  have  no  distinct  sensation 
for  either  separately.  Why  then  is  there  any  difference  in 
the  essence  of  the  two?  Why  not  consider  them  both  as 
brought  into  our  equations  by  the  agency  of  mathematical 
transformations?  This  is  Einstein's  point  of  view. 

Granting,  then,  the  principle  of  equivalence,  we  can  so 
choose  axes  at  any  point  at  any  instant  that  the  gravitational 
field  will  disappear;  these  axes  are  therefore  of  what  Edding- 
ton  calls  the  "Galilean"  type,  the  simplest  possible.  Con- 
sider, that  is,  an  observer  in  a  box,  or  compartment,  which  is 
falling  with  the  acceleration  of  the  gravitational  field  at  that 
point.  He  would  not  be  conscious  of  the  field.  If  there  were 
a  projectile  fired  off  in  this  compartment,  the  observer  would 
describe  its  path  as  being  straight.  In  this  space  the  infinites- 
imal interval  between  two  space-time  points  would  then  be 
given  by  the  formula 

ds*  =  dx\+dx\+dx*a+dx24, 

where  ds  is  the  interval  and  Xi,  xz,  #3,  #4,  are  coordinates.  If 
we  make  a  mathematical  transformation,  i.e.,  use  another  set 
of  axes,  this  interval  would  obviously  take  the  form 


ds*  — 
where  x\t  3%,  £3  and  x\  are  now  coordinates  referring  to  the  new 


Appendix  105 


axes.    This  relation  involves  ten  coefficients,  the  coefficients 
defining  the  transformation. 

But  of  course  a  certain  dynamical  value  is  also  attached  to 
the  g's,  because  by  the  transfer  of  our  axes  from  the  Galilean 
type  we  have  made  a  change  which  is  equivalent  to  the  intro- 
duction of  a  gravitational  field;  and  the  g's  must  specify  the 
field.  That  is,  these  g's  are  the  expressions  of  our  experiences, 
and  hence  their  values  can  not  depend  upon  the  use  of  any 
special  axes;  the  values  must  be  the  same  for  all  selections. 
In  other  words,  whatever  function  of  the  coordinates  any  one  g 
is  for  one  set  of  axes,  if  other  axes  are  chosen,  this  g  must  still 
be  the  same  function  of  the  new  coordinates.  There  are  ten 
g's  defined  by  differential  equations;  so  we  have  ten  co variant 
equations.  Einstein  showed  how  these  g's  could  be  regarded 
as  generalized  potentials  of  the  field.  Our  own  experiments 
and  observations  upon  gravitation  have  given  us  a  certain 
knowledge  concerning  its  potential;  that  is,  we  know  a  value 
for  it  which  must  be  so  near  the  truth  that  we  can  properly 
call  it  at  least  a  first  approximation.  Or,  stated  differently,  if 
Einstein  succeeds  in  deducing  the  rigid  value  for  the  gravi- 
tational potential  in  any  field,  it  must  degenerate  to  the  New- 
tonian value  for  the  great  majority  of  cases  with  which  we  have 
actual  experience.  Einstein's  method,  then,  was  to  investigate 
the  functions  (or  equations)  which  would  satisfy  the  mathe- 
matical conditions  just  described.  A  transformation  from 
the  axes  used  by  the  observer  in  the  following  box  may  be 
made  so  as  to  introduce  into  the  equations  the  gravitational 
field  recognized  by  an  observer  on  the  earth  near  the  box; 
but  this,  obviously,  would  not  be  the  general  gravitational 
field,  because  the  field  changes  as  one  moves  over  the  surface 
of  the  earth.  A  solution  found,  therefore,  as  just  indicated, 
would  not  be  the  one  sought  for  the  general  field;  and  another 


106  Appendix 


must  be  found  which  is  less  stringent  than  the  former  but 
reduces  to  it  as  a  special  case.  He  found  himself  at  liberty 
to  make  a  selection  from  among  several  possibilities,  and 
for  several  reasons  chose  the  simplest  solution.  He  then 
tested  this  decision  by  seeing  if  his  formulae  would  degenerate 
to  Newton's  law  for  the  limiting  case  of  velocities  small  when 
compared  with  that  of  light,  because  this  condition  is  satisfied 
in  those  cases  to  which  Newton's  law  applies.  His  formulae 
satisfied  this  test,  and  he  therefore  was  able  to  announce  a 
"law  of  gravitation,"  of  which  Newton's  was  a  special  form 
for  a  simple  case. 

To  the  ordinary  scholar  the  difficulties  surmounted  by  Ein- 
stein in  his  investigations  appear  stupendous.  It  is  not  im- 
probable that  the  statement  which  he  is  alleged  to  have  made 
to  his  editor,  that  only  ten  men  in  the  world  could  under- 
stand his  treatment  of  the  subject,  is  true.  I  am  fully  pre- 
pared to  believe  it,  and  wish  to  add  that  I  certanily  am  not 
one  of  the  ten.  But  I  can  also  say  that,  after  a  careful  and 
serious  study  of  his  papers,  I  feel  confident  that  there  is  nothing 
in  them  which  I  can  not  understand,  given  the  time  to  become 
familiar  with  the  special  mathematical  processes  used.  The 
more  I  work  over  Einstein's  papers,  the  more  impressed  I  am, 
not  simply  by  his  genius  in  viewing  the  problem,  but  also  by 
his  great  technical  skill. 

Following  the  path  outlined,  Einstein,  as  just  said,  arrived 
at  certain  mathematical  laws  for  a  gravitational  field,  laws 
which  reduced  to  Newton's  form  in  most  cases  where  observa- 
tions are  possible,  but  which  led  to  different  conclusions  in  a 
few  cases,  knowledge  concerning  which  we  might  obtain  by 
careful  observations.  I  shall  mention  a  few  deductions  from 
Einstein's  formulae. 

1.  If  a  heavy  particle  is  put  at  the  center  of  a  circle,  and,  if 


Appendix  107 


108  Appendix 


that  there  was  actually  such  a  change  as  just  described  in  the 
orbit  of  Mercury,  amounting  to  574"  of  arc  per  century; 
and  it  has  been  shown  that  of  this  a  rotation  of  532"  was  due 
to  the  direct  action  of  other  planets,  thus  leaving  an  unex- 
plained rotation  of  42"  per  century.  Einstein's  formulae 
predicted  a  rotation  of  43",  a  striking  agreement. 

4.  In  accordance  with  Einstein's  formulae  a  ray  of  light 
passing  close  to  a  heavy  piece  of  matter,  the  sun,  for  instance, 
should  experience  a  sensible  deflection  in  towards  the  sun. 
This  might  be  expected  from  "general"  consideration  of 
energy  in  motion;  energy  and  mass  are  generally  considered 
to  be  identical  in  the  sense  that  an  amount  of  energy  E  has 
the  mass  Elcz  where  c  is  the  velocity  of  light;  and  conse- 
quently a  ray  of  light  might  fall  within  the  province  of  gravi- 
tation and  the  amount  of  deflection  to  be  expected  could  be 
calculated  by  the  ordinary  formula  for  gravitation.  Another 
point  of  view  is  to  consider  again  the  observer  inside  the  com- 
partment falling  with  the  acceleration  of  the  gravitational 
field.  To  him  the  path  of  a  projectile  and  a  ray  of  light  would 
both  appear  straight;  so  that,  if  the  projectile  had  a  velocity 
equal  to  that  of  light,  it  and  the  light  wave  would  travel  side 
by  side.  To  an  obesrver  outside  the  compartment,  e.g.,  to 
one  on  the  earth,  both  would  then  appear  to  have  the  same 
deflection  owing  to  the  sun.  But  how  much  would  the 
path  of  the  projectile  be  bent?  What  would  be  the  shape  of 
its  parabola?  One  might  apply  Newton's  law;  but,  accord- 
ing to  Einstein's  formulae,  Newton's  law  should  be  used  only 
for  small  velocities.  In  the  case  of  a  ray  passing  close  to  the 
sun  it  was  decided  that  according  to  Einstein's  formula  there 
should  be  a  deflection  of  1".75  whereas  Newton's  law  of 
gravitation  predicted  hah*  this  amount.  Careful  plans  were 
made  by  various  astronomers,  to  investigate  this  question  at 


Appendix  109 


the  solar  eclipse  last  May,  and  the  result  announced  by  Dyson, 
Eddington  and  Crommelin,  the  leaders  of  astronomy  in  Eng- 
land, was  that  there  was  a  deflection  of  1".9.  Of  course  the 
detection  of  such  a  minute  deflection  was  an  extraordinarily 
difficult  matter,  so  many  corrections  had  to  be  applied  to  the 
original  observations;  but  the  names  of  the  men  who  record 
the  conclusions  are  such  as  to  inspire  confidence.  Certainly 
any  effect  of  refraction  seems  to  be  excluded. 

It  is  thus  seen  that  the  formulae  deduced  by  Einstein  have 
been  confirmed  in  a  variety  of  ways  and  in  a  most  brilliant 
manner.  In  connection  with  these  formulae  one  question 
must  arise  in  the  minds  of  everyone;  by  what  process,  where 
in  the  course  of  the  mathematical  development,  does  the  idea 
of  mass  reveal  itself?  It  was  not  in  the  equations  at  the 
beginning  and  yet  here  it  is  at  the  end.  How  does  it  appear? 
As  a  matter  of  fact  it  is  first  seen  as  a  constant  of  integration 
in  the  discussion  of  the  problem  of  the  gravitational  field 
due  to  a  single  particle;  and  the  identity  of  this  constant 
with  mass  is  proved  when  one  compares  Einstein's  formulae 
with  Newton's  law  which  is  simply  its  degenerated  form. 
This  mass,  though,  is  the  mass  of  which  we  become  aware 
through  our  experiences  with  weight;  and  Einstein  proceeded 
to  prove  that  this  quantity  which  entered  as  a  constant  of 
integration  in  his  ideally  simple  problem  also  obeyed  the  laws 
of  conservation  of  mass  and  conservation  of  momentum  when 
he  investigated  the  problems  of  two  and  more  particles. 
Therefore  Einstein  deduced  from  his  study  of  gravitational 
fields  the  well-known  properties  of  matter  which  form  the 
basis  of  theoretical  mechanics.  A  further  logical  consequence 
of  Einstein's  development  is  to  show  that  energy  has  mass,  a 
concept  with  which  every  one  nowadays  is  familiar. 

The  description  of  Einstein's  method  which  I  have  given  so 


110  Appendix 


far  is  simply  the  story  of  one  success  after  another;  and  it  is 
certainly  fair  to  ask  if  we  have  at  last  reached  finality  in  our 
investigation  of  nature,  if  we  have  attained  to  truth.  Are 
there  no  outstanding  difficulties?  Is  there  no  possibility  of 
error?  Certainly,  not  until  all  the  predictions  made  from 
Einstein's  formulae  have  been  investigated  can  much  be  said; 
and  further,  it  must  be  seen  whether  any  other  lines  of  argu- 
ment will  lead  to  the  same  conclusions.  But  without  waiting 
for  all  this  there  is  at  least  one  difficulty  which  is  apparent 
at  this  time.  We  have  discussed  the  laws  of  nature  as  inde- 
pendent in  their  form  of  reference  axes,  a  concept  which  appeals 
strongly  to  our  philosophy;  yet  it  is  not  at  ah1  clear,  at  first 
sight,  that  we  can  be  justified  in  our  belief.  We  can  not 
imagine  any  way  by  which  we  can  become  conscious  of  the 
translation  of  the  earth  in  space;  but  by  means  of  gyroscopes 
we  can  learn  a  great  deal  about  its  rotation  on  its  axis.  We 
could  locate  the  positions  of  its  two  poles,  and  by  watching  a 
Foucault  pendulum  or  a  gyroscope  we  can  obtain  a  number 
which  we  interpret  as  the  angular  velocity  of  rotation  of  axes 
fixed  in  the  earth;  angular  velocity  with  reference  to  what? 
Where  is  the  fundamental  set  of  axes  ?  This  is  a  real  difficulty. 
It  can  be  surmounted  in  several  ways.  Einstein  himself  has 
outlined  a  method  which  in  the  end  amounts  to  assuming 
the  existence  on  the  confines  of  space  of  vast  quantities  of 
matter,  a  proposition  which  is  not  attractive.  deSitter  has 
suggested  a  peculiar  quality  of  the  space  to  which  we  refer 
our  space-time  coordinates.  The  consequences  of  this  are 
most  interesting,  but  no  decision  can  as  yet  be  made  as  to  the 
justification  of  the  hypothesis.  In  any  case  we  can  say  that 
the  difficulty  raised  is  not  one  that  destroys  the  real  value  of 
Einstein's  work. 

In  conclusion  I  wish  to  emphasize  the  fact,  which  should 


Appendix  111 


be  obvious,  that  Einstein  has  not  attempted  any  explanation 
of  gravitation;  he  has  been  occupied  with  the  deduction  of  its 
laws.  These  laws,  together  with  those  of  electromagnetic 
phenomena,  comprise  our  store  of  knowledge.  There  is  not 
the  slightest  indication  of  a  mechanism,  meaning  by  that  a 
picture  in  terms  of  our  senses.  In  fact  what  we  have  learned 
has  been  to  realize  that  our  desire  to  use  such  mechanisms  is 
futile. 


THE  REFLECTION  OF  LIGHT  BY  GRAVITATION 

AND   THE  EINSTEIN  THEORY 

OF  RELATIVITY.* 

SIR  FRANK  DYSON 
the  Astronomer  Royal 

The  purpose  of  the  expedition  was  to  determine  whether 
any  displacement  is  caused  to  a  ray  of  light  by  the  gravitational 
field  of  the  sun,  and  if  so,  the  amount  of  the  displacement. 
Einstein's  theory  predicted  a  displacement  varying  inversely 
as  the  distance  of  the  ray  from  the  sun's  center,  amounting 
to  1".75  for  a  star  seen  just  grazing  the  sun.  .  . 

"A  study  of  the  conditions  of  the  1919  eclipse  showed  that 
the  sun  would  be  very  favorably  placed  among  a  group  of 
bright  stars — in  fact,  it  would  be  in  the  most  favorable  possi- 
ble position.  A  study  of  the  conditions  at  various  points 
on  the  path  of  the  eclipse,  in  which  Mr.  Hinks  helped  us, 
pointed  to  Sobral,  in  Brazil,  and  Principe,  an  island  off  the 
west  coast  of  Africa,  as  the  most  favorable  stations.  .  . 

The  Greenwich  party,  Dr.  Crommelin  and  Mr.  Davidson, 
reached  Brazil  in  ample  time  to  prepare  for  the  eclipse,  and 
the  usual  preliminary  focusing  by  photographing  stellar 
fields  was  carried  out.  The  day  of  the  eclipse  opened  cloudy, 
but  cleared  later,  and  the  observations  were  carried  out  with 
almost  complete  success.  With  the  astrographic  telescope 
Mr.  Davidson  secured  15  out  of  18  photographs  showing  the 
required  stellar  images.  Totality  lasted  6  minutes,  and  the 
average  exposure  of  the  plates  was  5  to  6  seconds.  Dr. 

*  From  a  report  In  The  Observatory,  of  the  Joint  Eclipse  Meeting 
of  the  Royal  Society  and  the  Royal  Astronomical  Society, 
NoTember  6, 1919. 


Appendix  113 


Oommelin  with  the  other  lens  had  7  successful  plates  out  of  8. 
The  unsuccessful  plates  were  spoiled  for  this  purpose  by  the 
clouds,  but  show  the  remarkable  prominence  very  well. 

When  the  plates  were  developed  the  astrographic  images 
were  found  to  be  out  of  focus.  This  is  attributed  to  the  effect 
of  the  sun's  heat  on  the  coelostat  mirror.  The  images  were 
fuzzy  and  quite  different  from  those  on  the  check-plates 
secured  at  night  before  and  after  the  eclipse.  Fortunately 
the  mirror  which  fed  the  4-inch  lens  was  not  affected,  and  the 
star  images  secured  with  this  lens  were  good  and  similar  to 
those  got  by  the  night-plates.  The  observers  stayed  on  in 
Brazil  until  July  to  secure  the  field  in  the  night  sky  at  the 
altitude  of  the  eclipse  epoch  and  under  identical  instrumental 
conditions. 

The  plates  were  measured  at  Greenwich  immediately  after 
the  observers'  return.  Each  plate  was  measured  twice  over 
by  Messrs.  Davidson  and  Furner,  and  I  am  satisfied  that  such 
faults  as  lie  in  the  results  are  in  the  plates  themselves  and  not 
in  the  measures.  The  figures  obtained  may  be  briefly  sum- 
marized as  follows:  The  astrographic  plates  gave  0".97  for 
the  displacement  at  the  limb  when  the  scale-value  was  deter- 
mined from  the  plates  themselves,  and  1".40  when  the  scale- 
value  was  assumed  from  the  check  plates.  But  the  much 
better  plates  gave  for  the  displacement  at  the  limb  I". 98, 
Einstein's  predicted  value  being  I". ,75.  Further,  for  these 
plates  the  agreement  was  all  that  could  be  expected.  .  .  . 

After  a  careful  study  of  the  plates  I  am  prepared  to  say  that 
there  can  be  no  doubt  that  they  confirm  Einstein's  prediction. 
A  very  definite  result  has  been  obtained  that  light  is  deflected 
according  to  Einstein's  law  of  gravitation. 


114  Appendix 


PROFESSOR  A.  S.  EDDINGTON 
Royal  Observatory 

Mr.  Cottingham  and  I  left  the  other  observers  at  Madeira 
and  arrived  at  Principe  on  April  23.  ...  We  soon  realiz 
that  the  prospect  of  a  clear  sky  at  the  end  of  May  was  not  very 
good.  Not  even  a  heavy  thunderstorm  on  the  morning  of  1 
eclipse,  three  weeks  after  the  end  of  the  wet  season,  saved  1 
situation.  The  sky  was  completely  cloudy  at  first  contact 
but  about  half  an  hour  before  totality  we  began  to  see  glimp 
of  the  sun's  crescent  through  the  clouds.  We  carried  out  on 
program  exactly  as  arranged,  and  the  sky  must  have 
clearer  towards  the  end  of  totality.  Of  the  16  plates  taken 
during  the  five  minutes  of  totality  the  first  ten  showed  no  stars 
at  all;  of  the  later  plates  two  showed  five  stars  each,  from  which 
a  result  could  be  obtained.  Comparing  them  with  the  check- 
plates  secured  at  Oxford  before  we  went  out,  we  obtained  as 
the  final  result  from  the  two  plates  for  the  value  of  the  displace- 
ment of  the  limb  1".6±O.S  .  .  .  This  result  supports  the 
figures  obtained  at  Sobral.  .  .  . 

I  will  pass  now  to  a  few  words  on  the  meaning  of  the  result. 
It  points  to  the  larger  of  the  two  possible  values  of  the  deflec- 
tion. The  simplest  interpretation  of  the  bending  of  the  ray 
is  to  consider  it  as  an  effect  of  the  weight  of  light.  We  know 
that  momentum  is  carried  along  on  the  path  of  a  beam  of  light. 
Gravity  in  acting  creates  momentum  in  a  direction  different 
from  that  of  the  path  of  the  ray  and  so  causes  it  to  bend.  For 
the  half -effect  we  have  to  assume  that  gravity  obeys  Newton's 
law;  for  the  full  effect  which  has  been  obtained  we  must 
assume  that  gravity  obeys  the  new  law  proposed  by  Einstein. 
This  is  one  of  the  most  crucial  tests  between  Newton's  law 
and  the  proposed  new  law.  Einstein's  law  had  already  indi- 
cated a  perturbation,  causing  the  orbit  of  Mercury  to  revolve. 


Appendix  115 


That  confirms  it  for  relatively  small  velocities.  Going  to  the 
limit,  where  the  speed  is  that  of  light,  the  perturbation  is 
increased  in  such  a  way  as  to  double  the  curvature  of  the 
path,  and  this  is  now  confirmed. 

This  effect  may  be  taken  as  proving  Einstein's  law  rather 
than  his  theory.  It  is  not  affected  by  the  failure  to  detect  the 
displacement  of  Fraunhofer  lines  on  the  sun.  If  this  latter 
failure  is  confirmed  it  will  not  affect  Einstein's  law  of  gravita- 
tion, but  it  will  affect  the  views  on  which  the  law  was  arrived 
at.  The  law  is  right,  though  the  fundamental  ideas  underly- 
ing it  may  yet  be  questioned.  .  .  . 

One  further  point  must  be  touched  upon.  Are  we  to 
attribute  the  displacement  to  the  gravitational  field  and  not 
to  the  refracting  matter  around  the  sun?  The  refractive  index 
required  to  produce  the  result  at  a  distance  of  15'  from  the 
sun  would  be  that  given  by  gases  at  a  pressure  of  WQ  to  afFo  of 
an  atmosphere.  This  is  of  too  great  a  density  considering 
the  depth  through  which  the  light  would  have  to  pass. 

Sm  J.  J.  THOMSON 
President  of  the  Royal  Society 

...  If  the  results  obtained  had  been  only  that  light  was 
affected  by  gravitation,  it  would  have  been  of  the  greatest 
importance.  Newton,  did,  in  fact,  suggest  this  very  point  in 
his  "Optics,"  and  his  suggestion  would  presumably  have  led 
to  the  half- value.  But  this  result  is  not  an  isolated  one;  it 
is  part  of  a  whole  continent  of  scientific  ideas  affecting  the  most 
fundamental  concepts  of  physics.  .  .  This  is  the  most  impor- 
tant result  obtained  in  connection  with  the  theory  of  gravita- 
tion since  Newton's  day,  and  it  is  fitting  that  it  should  be 


116  Appendix 


announced  at  a  meeting  of  the  society  so  closely  connected 
with  him. 

The  difference  between  the  laws  of  gravitation  of  Einstein 
and  Newton  come  only  in  special  cases.  The  real  interest  of 
Einstein's  theory  lies  not  so  much  in  his  results  as  in  the 
method  by  which  he  gets  them.  If  his  theory  is  right, 
it  makes  us  take  an  entirely  new  view  of  gravitation.  If  it  is 
sustained  that  Einstein's  reasoning  holds  good — and  it  has 
survived  two  very  severe  tests  in  connection  with  the  perihelion 
of  mercury  and  the  present  eclipse — then  it  is  the  result  of 
one  of  the  highest  achievements  of  human  thought.  The 
weak  point  in  the  theory  is  the  great  difficulty  in  expressing 
it.  It  would  seem  that  no  one  can  understand  the  new  law 
of  gravitation  without  a  thorough  knowledge  of  the  theory  of 
invariants  and  of  the  calculus  of  variations. 

One  other  point  of  physical  interest  arises  from  the  discus- 
sion. Light  is  deflected  in  passing  near  large  bodies  of  matter. 
This  involves  alterations  in  the  electric  and  magnetic  field. 
This,  again,  implies  the  existence  of  electric  and  magnetic 
forces  outside  matter — forces  at  present  unknown,  though 
some  idea  of  their  nature  may  be  got  from  the  results  of  this 
expedition. 


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